Ancient Science And Modern Civilization

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last rharked below. '

George Sarton

Ancient Science
and Modern Civilization

Euclid and His Time

Ptolemy and His Time

The End of Greek Science and Culture

HARPER TORCH BOOKS /Science Library

HARPER e> BROTHERS, PUBLISHERS

New York

ANCIENT SCIENCE AND MODERN CIVILIZATION

Copyright 1954 by University of Nebraska Press
Printed in the United States of America

Reprinted by arrangement with
University of Nebraska Press

All rights in this book are reserved.
No part of the book may be used or reproduced
in any manner whatsoever without written per-
mission except in the case of brief quotations
embodied in critical articles and reviews. For
information address Harper & Brothers
49 East 33rd Street, New York 16, N. Y.

First HARPER TORCHBOOK edition published 1959

CONTENTS

PREFACE

EUCLID AND HIS TIME 3

PTOLEMY AND HIS TIME 37

THE END OF GREEK SCIENCE AND CULTURE 75

Ancient Science
and Modern Civilization

PREFACE

This book reproduces the full text of the three Montgomery
Lectures which it was my privilege to deliver at the University
of Nebraska, in Lincoln, on April 19, 21, 23, 1954.

In spite of their name the "lectures" were not read but
spoken; the essential of the spoken and written texts is the
same, but there are naturally considerable differences in the
details. The spoken text is to the written one with its ex-
planatory footnotes like a fresco to a miniature. That must
be so, because people cannot listen as accurately as they can
read. I have explained my views on this subject many times,
last in the preface to my Logan Clendening Lecture on Galen
of Pergamon (University of Kansas Press, Lawrence, Kansas,
1954).

As mechanical progress discourages the printing of Greek
type, it has become necessary to transcribe the Greek words

ANCIENT SCIENCE AND MODERN CIVILIZATION

in our alphabet as exactly as possible. The diphthongs are
written as in Greek with the same vowels (e.g., ai not ae, ei not
i, oi not oe), except ou, which is written u to conform with
English pronunciation (by the way, the Greek ou is not a real
diphthong but a single vowel sound) . The omicron is always
replaced by an o, and hence the Greek names are not Latin-
ized but preserve their Greek look and sound. There is really
no reason for giving a Latin ending to a Greek name when one
is writing not in Latin but in English. Hence, we write
Epicures not Epicurus (the two u's of the Latin word repre-
sent different Greek vowels) . We indicate the differences be-
tween the short vowels epsilon and omicron and the long
ones eta and omega, as we have just done in their names.
Hence, we shall write Heron, Philon, but some names have
become so familiar to English readers that we must write them
in the English way. We cannot help writing Plato instead of
Platon and Aristotle instead of Aristoteles, etc. For more de-
tails, see my History of Science, p. xvii.

Indications such as (III-2 B.C.) or (II-l) after a name
mean two things: (1) the man flourished in the second half of
the third century before Christ or in the first half of the second
century; (2) he is dealt with in my Introduction.

GEORGE SARTON
Harvard University
Cambridge, Massachusetts

EUCLID AND HIS TIME

(first half of third century B.C.)

w,

HAT has ancient science to do with modern
civilization? one might ask. Very much. Modern civilization
is focused upon science and technology, and modern science
is but the continuation of ancient science; it would not exist
without the latter. For example, Euclid flourished in Alexan-
dria more than twenty-two centuries ago, and yet he is still
very much alive, and his name is equated with that of
geometry itself. What has happened to him happens to every
man whose name was equated with that of a thing; the thing
is known but the man himself is forgotten. When I was a
child, the table of multiplication was called the Table of
Pythagoras, but the teacher did not tell us who Pythagoras
was; perhaps she did not know it herself; she would have been

ANCIENT SCIENCE AND MODERN CIVILIZATION

a very wise person if she did. Pythagoras was simply a common
name to us like sandwich, mackintosh or macadam. Thus it
was wrong to say that Euclid is very much alive today; geome-
try is but not he. His name is very often on our lips, but who
was he? The purpose of my first lecture is to explain that, but
no man ever lives in a social vacuum, and to bring him back to
life we must, first of all, describe his environment. This is
something important which many historians of science shame-
fully neglect; it is foolish to speak of great men of science
without trying to explain their personality and their genius,
neither of which can be understood outside of the social en-
vironment wherein they developed.

1. THE ALEXANDRIAN RENAISSANCE

In the first volume of my History of Science, I have described
ancient science down to the end of Hellenic days. Euclid stands
at the beginning of a new age, absolutely different in many
respects from the preceding, and generally called the Hellenis-
tic Age. The word Hellenistic is well chosen, it suggests Hel-
lenism plus something else, foreign to it, Egyptian and oriental.

The break between those two ages, one of the greatest revo-
lutions or discontinuities in history, was caused by Alexander
the Great (IV-2 B.C.), who conquered a great part of the world
within twelve years, from 334 to his death in 323 at the ripe
age of thirty-three. As his armies were Greek, he carried Greek
culture into the very heart of Asia; it has been said that he
Hellenized Western Asia, but it could be said as well that he
helped to orientalize Eastern Europe. Many cities were
founded by him and bear a name derived from his, Alexandria,
some as far East as Sogdiana beyond the Oxus, or India

EUCLID AND HIS TIME

Superior beyond the Indus. By far the most important was
the one founded soon after his conquest of Egypt in 331.

The Greeks called that city Alexandreia he pros Aigypto
(Latin, Alexandria ad Aegyptum) and rightly so, because it
stood at the edge of Egypt and was very different from it. It
is as if we said that Hong Kong is near China. The com-
parison is useful, because, just as in Hong Kong the over-
whelming majority of the inhabitants are Chinese, we may as-
sume that in Alexandria the majority were native Egyptians.
The ruling class was Macedonian or Greek; as the city became
more prosperous, it attracted a great diversity of foreigners,
Ethiopians or Abyssinians and other Africans who came down
the Nile; Asiatics, primarily Jews, but also Syrians, Persians,
Arabs, Hindus. Alexandria soon became (and has remained
throughout the ages) one of the most cosmopolitan cities of the
world. Its harbor was and has remained the largest of the East-
ern Mediterranean Sea.

This suggests another comparison, which I find very help
ful, with New York. Alexandria's relationship to Athens in
ancient times was comparable to New York's relationship to
London. If one considers the speed of communication then
and now, the distances, Alexandria-Athens and New York-Lon-
don were about the same; New York was an offspring of
Europe, just as much as Alexandria. Finally, its cosmopoli-
tanism, and especially its Jewishness, make of it the American
Alexandria. The main difference is that New York is es-
sentially American, while Alexandria was definitely a Greek
colony.

Alexander died in Babylon in the middle of June 323 and
soon afterwards one of his closest companions, a Macedonian

ANCIENT SCIENCE AND MODERN CIVILIZATION

called Ptolemaios, son of Lagos, 1 became the governor or
master of Egypt; in 304 he proclaimed himself king and found-
ed the Ptolemaic dynasty, which lasted until 30 B.C. for three
centuries. Ptolemaios I Soter must have been a man of con-
siderable genius; not only was he the founder of a dynasty, but
he was a patron of science and arts and wrote what was per-
haps the best history of Alexander the Great. When he died
in 283/2, he was succeeded by his son, Ptolemaios II Philadel-
phos, who ruled until 246 and completed his father's task.
The Alexandrian Renaissance was mainly accomplished by
these two kings within the first half of the third century; I
introduced them both, because it is not always possible to
separate their achievements.

In order to create the new civilization in Alexandria, they
needed the help of other Greeks, not only soldiers and mer-
chants but also intellectuals of various kinds, administrators,
philosophers, teachers, poets, artists and men of science. Before
dealing with Euclid, it is well to speak of some of them.

In the first place, we shall speak of the architects, for to
build a new town in the Greek style such were needed. The
Greeks were great town builders and did not allow the new
cities to grow at random. The planning of Alexandria was
intrusted by Alexander or more probably by the first Ptole-
maios to Deinocrates of Rhodes, who was perhaps the most

1 The kings of that dynasty are often called Ptolemy; I prefer to use
the original Greek form Ptolemaios (plural, Ptolemaioi) , however, re-
serving the English form Ptolemy for a more illustrious person and one
of far greater international significance, the astronomer Ptolemy (II- 1) , to
whom my second lecture will be devoted. Hence, there will be no am-
biguity; when I write Ptolemy, the astronomer is meant, while Ptolemaios
is only a king.

EUCLID AND HIS TIME

eminent architect of his time. He it was who designed the
new temple of Artemis at Ephesos, and he had conceived the
idea of cutting one of the peaks of Mt. Athos in the shape of
a gigantic statue of Alexander. The other architect, Sostratos
of Cnidos, built a lighthouse on a little island in the harbor.
The island was called Pharos, and therefore the lighthouse
received the same name. 2 It was the earliest lighthouse to be
definitely known and described. A tower of about four
hundred feet high, it could be seen over the plains or the sea
from a long distance. It became so famous that it was generally
listed as one of the seven wonders of the world.

The pharos was an outstanding symbol of Alexandrian
prosperity; two institutions, the Museum and the Library,
illustrated the greatness of Alexandrian culture.

There had been museums before in Greece, because a

*

museum was simply a temple dedicated to the Muses, the nine
goddesses of poetry, history and astronomy, but this museum
was a new kind of institution which was so noteworthy that its
name was preserved and has been incorporated into many
languages. The meaning has changed, however, and museums
all over the world are primarily buildings containing exhibi-
tions of art, archaeology, natural history, etc. A certain
amount of teaching and research is connected with the best of
them; yet the Alexandrian exemplar was very different. If we
had to describe its function in modern language, we would
say that the Museum of Alexandria was primarily an institute
for scientific research. It probably included dormitories for
the men of science, their assistants and disciples, assembly

2 Later the name was given to any lighthouse; it was transcribed with
the same meaning in Latin and many Romance languages (L. farus, F.
phare, It. and Sp. faro, Port, farol or pharol, etc.) .

ANCIENT SCIENCE AND MODERN CIVILIZATION

rooms, roofed colonnades for open-air study or discussion,
laboratories, an observatory, botanical and zoological gardens.
The Museum did not include all these features at the begin-
ning, but like every institution, it grew in size and com-
plexity as long as it was actually flourishing. Its scientific de-
velopment owed much to its royal patrons and even more to
Straton, who had been a pupil of Theophrastos. Straton was
called to Alexandria by the first Ptolemaios (c. 300); we may
call him the real founder of the Museum for he brought to it
the intellectual atmosphere of the Lyceum, and it was thanks
tc him that it became not a school of poetry and eloquence,
but an institute of scientific research. Straton was so deeply
interested in the study of nature that he was nicknamed ho
physicos, the physicist. Under the distant influence of Aristotle
and the closer one of his own master, he realized that no
progress is possible except on a scientific basis and he stressed
the physical (vs. the metaphysical) tendencies of the Lyceum.
He remained in Egypt many years, perhaps as many as twelve,
or even more, being finally recalled to Athens when Theo-
phrastos died in 288; he was appointed president or head-
master of the Lyceum (the third one) and directed it for about
eighteen years (c. 288-c. 270). It is pleasant to think of the
Museum being organized by an alumnus of the Lyceum, who
later became its very head.

Much was done at the Museum during the first century of
its existence. Mathematical investigations were led by Euclid,
Eratosthenes of Gyrene, who was first to measure the size of
the earth and did it with remarkable precision, Apollonios of
Perga, who composed the first textbook on conies. Another
contemporary giant, Archimedes, flourished in Syracuse, but
he may have visited Alexandria and he was certainly influenced

8

EUCLID AND HIS TIME

by its mathematical school. The astronomical work was equally
remarkable. Alexandria was an ideal place for astronomical
syncretism; Greek, Egyptian and Babylonian ideas could mix
freely, in the first place, because there were no established tradi-
tions, no "vested interests" of any kind, and secondly, because
representatives of various races and creeds could and did
actually meet. Astronomical observations were made by Aris-
tyllos and Timocharis, and a little later by Conon of Samos;
the last-named used and discussed Babylonian observations of
eclipses. Meanwhile, another Samosian, Aristarchos, was not
only making observations of his own but defending theories
of such boldness that he has been called "the Copernicus of
antiquity."

The anatomical investigations carried through in the
Museum were .equally bold and fertile. Herophilos of dial-
cedon might be called the first scientific anatomist. He was
flourishing under Ptolemaios Soter, and it was probably he who
devised the ambitious program of anatomical research, an
elaborate survey of the human body on the basis of dissections.
As this was done systematically for the first time, the men in
charge were bound to make as many discoveries as an ex-
plorer who would happen to be the first to visit a new con-
tinent. Herophilos was the main investigator and the catalogue
of his observations is so long that it reads like the table of
contents of an anatomical textbook. He obtained the help of
another Greek, somewhat younger than himself, Erasistratos of
Ceos, who continued the anatomical survey and paid more
attention to physiology. It was claimed by Celsus (1-1) and
by church fathers who were eager to discredit pagan science
that the Alexandrian anatomists were not satisfied with the
dissection of dead bodies but obtained permission to dissect

ANCIENT SCIENCE AND MODERN CIVILIZATION

the bodies of living men, in order to have a better understand-
ing of the functioning of the organs. The story as told by
Celsus is plausible. We must bear in mind that the sensi-
bility of the ancients was less keen than ours and that the
Alexandrian anatomists were not hindered by religious or
social restrictions. As far as we know, medicine was not in-
cluded in the Museum program of research. It is possible that
Straton or Herophilos decided that medicine was too much of
an art to reward purely scientific research; the time was not
yet ripe for "experimental medicine."

Much of the work accomplished in mathematics, astronomy,
mathematical geography, anatomy and physiology was analy-
tical. With the exception of Euclid's Elements, the men of
science wrote what we would call monographs, such as would
be published today not in independent books but in journals.
This reminds us of the cardinal fact that the Alexandrian
Renaissance was a complete renaissance. At the beginning, I
remarked that the discontinuity and the revolution following
it were created by Alexander the Great. There is another
aspect of this which deserves emphasis. A deeper discontinuity
had been caused in the time of Alexander's youth by another
Macedonian but a greater man than himself, his tutor, Aris-
totle. One ought to say Aristotle the Great and Alexander the
Less. Aristotle was a philosopher, a man of science, an
encyclopaedist who tried to organize and to unify the whole of
knowledge. Considering his time and circumstances, his
achievements are astounding and many of the results attained
by him kept their validity for two thousand years. The con-
quests of Alexander were ephemeral; those of Aristotle were
durable and exceedingly fertile. After the master's death, his

10

EUCLID AND HIS TIME

disciples in Athens and even more so those of Alexandria
realized that the best way, nay, the only way of improving the
Aristotelian synthesis was by means of analysis.

As opposed to the fourth century in Athens, the Alexandrian
Renaissance was a period of analysis and research. This is an
outstanding example of one of the fundamental rhythms of
progress: analysis, synthesis, analysis, synthesis, and so on in-
definitely.

Of the two leading institutions the one of greater interest
to historians of science is the Museum. But it is probable that
the Library was an integral part of the Museum (even as every
research institute has a library of its own) ; both institutions
were included in the royal city or enclosure; both were royal
institutions, in 'the same way that they would be government
ones today, for the king was the state, and everything done for
the public good was done at the royal initiative and expense or
not at all. The Museum and its Library were public utilities.

An elaborate study of the Library has recently been pub-
lished by Dr. Parsons, 3 who has put together all the documents
available, but in spite of his zeal and ingenuity, our knowledge
of it is still very fragmentary. Many questions are still un-
answerable. The first organizer as well as the first collector
was almost certainly Demetrios of Phaleron, who worked hand
in glove with the first king and was probably clever enough
to give his royal patron the feeling of being the real creator.
Dr. Parsons gives us a list of the "librarians" beginning with
Demetrios and ending with the eighth one, Aristarchos of

Edward Alexander Parsons, The Alexandrian Library, Glory of the
Hellenic World. Its Rise, Antiquities and Destruction (New Yoik, Elsevier,
1952; Isis 43, 286).

11

ANCIENT SCIENCE AND MODERN CIVILIZATION

Samothrace (in 145 B.C.), which is very interesting in spit*
of the many conjectures which are implied. The mair
conclusion that one can draw from it is that the perioc
of creative activity of the Library lasted only one and a
half centuries (otherwise we would know the names of latei
librarians) ; this period was also that of greatest commercial
prosperity. After the second century B.C., the Library de
clined and fell into somnolence. At the time of its climax, il
had been exceedingly rich. It may have contained 400,OOC
"rolls." But it is impossible to be sure, not only because the
sources are lacking but also because the counting of rolls and
books is not as simple an operation, nor the total result as
determined, as one might think. It was not by any means the
earliest library, but it was by far the largest one of antiquit)
and found no equal perhaps until the tenth century when ver)
large collections of books became available in the Muslim
world, both East in Baghdad and West in Cordova. 4 By the
middle of the third century, the Library of Alexandria was
already so large that the creation of a new library, or call it
"branch" library, was found to be necessary. This was the
Serapeion, which earned some fame of its own, especially in
Roman times.

The Library suffered many vicissitudes. It may have been
damaged (or many books lost) in 48 B.C., when Caesar was
obliged to set fire to the Egyptian fleet in the harbor nearby.
A few years later, in 40, Anthony is said to have given to

* For the Baghdad libraries, see their catalogue, Fihrist al-'ulum, written
in 987 (see my Introduction to the History of Science [? vols., Baltimore
Carnegie Institution of Washington, 1927-48] 1, 662) ; the Cordova library
was gathered mainly by the caliph al-Hakam II, who died in 976 (Intro. 1,
658). It is curious that these two libraries date from the same time (X-2).

12

EUCLID AND HIS TIME

Cleopatra the library of Pergamon, but did that really hap-
pen? At the time of the Jewish historian Joseph (1-2) both
libraries were still very rich. Decadence was rapid during the
second century and there is good reason for believing that
many books (as well as other things) were taken to Rome.
Under Aurelian (Emperor, 270-75) the Museum and the
mother Library ceased to exist; the Serapeion then became the
main Library and the last refuge of pagan culture. In 391,
Theophilos (Bishop of Alexandria, 385-412), wishing to put
an end to paganism, destroyed the Serapeion; it is possible,
however, that the destruction was not complete and that many
books could be saved in one way or another. Not a great many,
however, if we believe Orosius' account of c. 416. When the
Muslims sacked Alexandria in 646, it is claimed that they des-
troyed the Library; that can only mean that they destroyed the
little that was left of it. The story of the great library, if it
could be told with precision, would be a history of the de-
cadence and fall of Alexandrian (pagan) culture. This cannot
be done, but it is certain that the climax was long past before
the age of Christ.

Let us return to its golden days. The Library was the main
center of information for every department, but for the
humanities it was much more than that: it was the brain and
heart of every literary and historical study. The astronomers
observed the heavens and measured the Earth, the anatomists
dissected human bodies. But the primary materials of his-
torians and philologists were in the library books and nowhere

else.

The librarians had not as easy a task as their colleagues
of today, who deal almost exclusively with printed books, each
of which is a very tangible object. The first technical librarian,

13

ANCIENT SCIENCE AND MODERN CIVILIZATION

Zenodotos of Ephesos, had to identify the rolls and put to-
gether those which belonged together, for example, the rolls
of the Iliad and Odyssey. He was, in fact, the first scientific
editor of those epics. The same process had to be followed
for all the rolls; they had to be investigated, one by one, identi-
fied, classified and finally edited as much as possible; it was
necessary to establish the text of each author and to de-
termine canons the Homeric one, the Hippocratic, etc. In
other words, Zenodotos and his followers were not only li-
brarians, but philologists. Callimachos of Gyrene, poet and
scholar, came to Alexandria before the middle of the third
century and was employed in making a catalogue of the library,
the Pinaces, which was the earliest work of its kind. 5 It was
very large, for it filled 120 rolls. Would that it had been pre-
served! Our knowledge of ancient literature, 'chiefly but not
exclusively Greek, would have been much greater than it is.
Indeed, a great many of the books which were available to
Alexandrian scholars have long ceased to exist; we often know
the names of the authors and the titles of the lost books; in
some favorable cases, extracts have been transmitted to us in
other books; in exceptional cases, the whole books have been
preserved.

Many historians used the Library of Alexandria; one of the
first to do so, perhaps, was the first king when he composed the
life of Alexander. A curious case was that of Manethon, who

B Some lists of Sumerian writings are considerably older but very short
(see my A History of Science: Ancient Science through the Golden Age of
Greece [Cambridge, Harvard University Press, 1952] I, 96). Whenever a
large number of tablets was kept together, some kind of list may have
proved necessary, but such lists were so rudimentary as compared with
Callimachos' catalogue raisonnd that the term catalogue as applied to
them is figurative.

14

EUCLID AND HIS TIME

wrote Annals of Egypt in Greek on the basis of Egyptian docu-
ments (whether these existed in the Library or in Temples
cannot be ascertained). The great geographer Eratosthenes who
was Librarian (the only man of science to hold that position,
but he was also a distinguished man of letters) realized the
essential need of historical research, scientific chronology.
When one deals with a single country, say, Egypt, a precise
dynastic history such as Manethon had tried to produce may
be sufficient, but when one has to study many countries, one
must be able to correlate their national chronologies, and this
is not possible unless one has a chronological frame applying
to all of them. The first such frame had been imagined by the
Sicilian Timaios, who suggested using the Olympic games as
references. Those games had become international events in
the Greek-speaking world and were of such importance that
we may assume that foreigners would attend them occasionally;
they occurred every fourth year from 776 on and hence might
provide an international scale. 6 It is not clear whether Timaios
was ever in touch with the historians of the Museum, and
whether Eratosthenes improved his invention. The Olympic
scale was introduced too late (beginning of the third century
B.C.) to remain long in use, because the rulers of the Western
world replaced it by another scale (A.U.C., from the founda-
tion of Rome in 753 B.C.), and it was completely superseded
in the course of time by the Christian and the Muslim

The numbering of the games began with those of 776, but many had
occurred before. A list of the Olympic winners has been preserved by
Eusebios (IV-1); it extends from 776 B.C. to 217 A.D., almost a millenium
(994 years). The Olympic era was used only by a few scholars, such as
Polybios (II-l B.C.) and Castor of Rhodes (1-1 B.C.); the Greek cities
continued to date events with reference to their own magistrates and,
moreover, they used different calendars.

15

ANCIENT SCIENCE AND MODERN CIVILIZATION

eras. 7 The point to bear in mind is that scientific chronology
began in Alexandria; Eratosthenes' interest in it is comparable
to his interest in geographical coordinates which are of the
same necessity in a two-dimensional continuum (a spherical
surface) as fixed dates along the line of time.

The identification of texts and their establishment opened
the door to every branch of philology, in the first place, gram-
mar. Not only was grammar needed to determine the sense
of a text without ambiguity but in a polyglot city like Alex-
andria it became necessary for the teaching of Greek to for-
eigners. Erastosthenes was the first man to call himself
philologist (philologos). Aristophanes of Byzantion (II-l B.C.)
and Aristarchos of Samothrace (II-l B.C.) were the first gram-
marians stricto scnsu. 8 Both were librarians of the Museum,
Aristophanes from 195 to 180, Aristarchos from c. 160 to 143
(or 131?). The earliest Greek grammar extant was composed

7 To summarize:
Ol. 1.1 776 B.C.
01. 2.1 77Ii B.C.

I I.C. 1 753 B.C. = Ol. 6.4.

B.C. 1 = 753 U.C. - 01. 194.4.

A.D. 1 754 U.C. = Ol. 195.1.

To make matters worse, a new Olympiad era was introduced by
Hadrian; it began when he dedicated the Olympieion in Athens: New Ol.
1= Ol. 227.3 = U.C. 884 A.D. 131.

8 Philology and in particular grammar are bound to occur when differ-
ent languages are used simultaneously, e.g., in the Mesopotamian and
Anatolian world (History of Science 1, 67) . In Greece proper, it developed
relatively late, because the language spoken in educated circles was rela-
tively pure and homogeneous. Nevertheless, grammar was a child of logic
and some grammatical functions were bound to be discovered as soon as
one attempted the logical analysis of any sentence (History of Science 1,
257, 579, 602).

* According to Parsons' list (p. 60), they were the sixth and eighth

16

EUCLID AND HIS TIME

by another Alexandrian, Dionysios Thrax (II-2 B.C.) . The
masterpieces of Greek literature were written before 300 B.C.,
the first grammar almost two centuries later. The fact that
the Hellenistic age witnessed the development of grammar as
well as the development of anatomy is a natural coincidence.
They were the fruits of the same analytical and scientific
mentality, applied in the first place to the language and, in
the second, to the body of man.

Euclid has long been waiting for us, and it is high time
that we return to him; yet, a few words should be said of the
most astonishing philological achievement of his time, the
Septuagint.

The name will explain itself in a moment. According to
the story told in Greek by the Jew Aristeas, 10 Demetrios of
Phaleron explained to King Ptolemaios II the need for trans-
lating the Torah into Greek. It is a fact that the large and
influential Jewish colony of Alexandria was losing its com-
mand of the Hebrew language; on the other hand, a Greek
version of the Torah might interest some of the Gentiles. The
king sent two ambassadors to the High Priest Eleazar in
Jerusalem, asking for Hebrew rolls of the Old Testament and
for six representatives of each tribe. The royal demand was
obeyed and seventy-two Jewish scholars were soon established
in the Pharos island and started their translation of the Holy
Scriptures. The translation might have been called Septuagin-
ta duo, but the second word was dropped. Aristeas' story was

director-librarians, the eighth being the last. The list is tentative and
suggests many objections, yet it is useful.

10 For more details, see the excellent edition and translation of the letter

of Aristeas to Philocrates by Moses Hadas (New York, Harper, 1951; Isis43,
287-88).

17

ANCIENT SCIENCE AND MODERN CIVILIZATION

embellished by later writers; the details of it do not matter.
The Torah was actually translated into Greek during the
third century. Other books of the Old Testament were trans-
lated later, many of them in the second century B.C., the last
one, Qoheleth (Ecclesiastes) not until about 100 A.D. 11

This Greek translation of the Old Testament is very im-
portant, because it was made upon the basis of a Hebrew text
more ancient than the Hebrew text which has been transmitted
to us. 12 Hence, any student of the Old Testament must know
Greek as well as Hebrew.

11 The original text of Qoheleth was produced very late, say, in the
period 250-168. This accounts for the exceptional lateness of its translation.
It was probably prepared c. 130 by Aquila, the Christianized disciple of
R. Akiba ben Joseph. It is not really a part of the Septuagint but of the
Version of Aquila (Intro. 1, 291). Practically the whole of the O.T. was
translated into Greek before the Christian era, and the name Septuagint
should be restricted to these pre-Christian versions.

12 It was believed that the Hebrew scrolls discovered by Beduins in
1947 in a cave along the western shore of the Dead Sea included earlier
readings than those reproduced in the Hebrew Bible. Isaiah and Habakkuk
scrolls and other fragments already deciphered do not sustain that belief,
for they do not seem to have a closer connection with the Septuagint text
than the Masoretic text has. The dating of those scrolls is very difficult,
but the arguments from paleography, archeology, radio-carbon testing, and
historical background would appear to fix the Mishnaic period at least
as well as any others. If more precision were desired, one might perhaps
say that the scrolls date from the century following the destruction of the
Second Temple and of the Jewish State in 70 A.D. Incidentally, the radio-
carbon dating is very inconclusive, because according to that method the
piece of linen used for wrapping dates from the period 33 A.D. 200.
There is already an abundant literature on the many problems raised by
those scrolls. For general information, see Harold Henry Rowley, The
Zadokite Fragments and the Dead Sea Scrolls (Oxford, Blackwell, 1952).
The writing of this footnote was made possible by the kindness of Abraham
A. Neuraan, president of Dropsie College in Philadelphia (letter dated
30 Nov., 1953).

18

EUCLID AND HIS TIME

The ancient Greeks had hardly paid any attention to the
queer people living in Palestine so near to their own colonies.
In Hellenistic times, this situation was reversed, because Greeks
and Jews were sharing the same environment in Egypt. This
was carried so far that Hellenistic scholars actually helped the
tradition of the Hebrew Scriptures.

2. EUCLID

And now, at last, let us consider Euclid 13 himself. We can
visualize very clearly his environment, the people and things
surrounding him, but who was he himself?

Unfortunately, our knowledge of him is very limited. This
is not an exceptional case. Mankind remembers the tyrants,
the successful politicians, the men of wealth, but it forgets its
true benefactors. How much do we know about Shakespeare?
I shall tell you all we know about Euclid, and that will not
take very long.

The places and dates of birth and death are unknown. He
was probably educated in Athens and, if so, received his mathe-
matical training at the Academy; he flourished in Alexandria
under the first Ptolemaios and possibly under the second. Two
anecdotes help to reveal his personality. It is said that the
king (Ptolemaios I) asked him "if there was in geometry any
shorter way than that of the Elements, and he answered that
there was no royal road to geometry." This is an excellent
story, which may not be true as far as Euclid is concerned
but has an eternal validity. Mathematics is "no respecter of

18 His name reads Eucleides, but it would be pedantic to use it in-
stead of Euclid, a proper name which has attained the dignity of a com-
mon name in our language. It is for the same reason (fear of pedantry)
that I shall write Ptolemy when speaking of the astronomer.

19

ANCIENT SCIENCE AND MODERN CIVILIZATION

persons." The other anecdote is equally good. "Someone who
had begun to read geometry with Euclid when he had learned
the first theorem asked him, 'But what shall I get by learning
these things?' Euclid called his slave and said, 'Give him an
obol, since he must gain out of what he learns.' "

Both anecdotes are recorded relatively late, the first by
Proclos, the second by Stobaios, both of whom lived in the
second half of the fifth century; they are plausible enough
and traditions of that homely kind would be tenacious.

Euclid was not officially connected with the Museum;
otherwise the fact would have been recorded. But if he
flourished in Alexandria, he was necessarily acquainted with
the Museum and the Library. As a pure mathematician, how-
ever, he did not need any laboratory and the manuscripts in
his own possession might have made him independent of the
Library. The number of manuscripts which he needed was
not considerable; a good student might easily copy the needed
texts during his school years. A mathematician does not need
many collaborators; like the poet, he does his best work alone,
very quietly. On the other hand, he may have been teaching a
few disciples; this would have been natural and is confirmed by
Pappos' remark that Apollonios of Perga (III-2 B.C.) was
trained in Alexandria by Euclid's pupils.

Euclid himself was so little known that he was confused
for a considerable time with the philosopher, Euclid of
Megara, 14 who had been one of Socrates' disciples (one of the

14 1 failed to devote a special note to him in my Introduction; he is
simply referred to in a footnote (/, 153) ; thus was an old tradition re-
versed. For a long time, Euclid of Alexandria was overshadowed by Euclid
of Megara; now the latter tends to be forgotten, because he is eclipsed by
the only Euclid whom everybody knows, the mathematician.

20

EUCLID AND HIS TIME

faithful who attended the master's death) , a friend of Plato's
and the founder of a philosophical school in Megara. The
confusion began very early and was confirmed by the early
printers until late in the sixteenth century. The first to correct
the error in an Euclidean edition was Federigo Commandino
in his Latin translation (Pesaro, 1572).

Euclid is thus like Homer. As everybody knows the Iliad
and the Odyssey, so does everybody know the Elements. Who
is Homer? He is the author of the Iliad. Who is Euclid? He is
the author of the Elements.

The Elements is the earliest textbook on geometry which
has come down to us. Its importance was soon realized and
thus the text has been transmitted to us in its integrity. It is
divided into thirteen books, which may be described briefly
as follows:

Books I to VI: Plane geometry. Book I is, of course,
fundamental; it includes the definitions and postulates and
deals with triangles, parallels, parallelograms, etc. The con-
tents of Book II might be called "geometrical algebra." Book
III: Geometry of the circle. Book IV: Regular polygons. Book
V: New theory of proportion applied to incommensurable as
well as commensurable quantities. Book VI: Applications of
the theory to plane geometry.

Books VII to X: Arithmetic, theory of numbers. Numbers
of many kinds, primes or prime to one another, least common
multiples, numbers in geometrical progression, etc. Book X,
which is Euclid's masterpiece, is devoted to irrational lines, all
the lines which can be represented by an expression, such as

wherein a and b are commensurable lines.

21

ANCIENT SCIENCE AND MODERN CIVILIZATION

Books XI-XIII: Solid geometry. Book XI is very much like
Books I and VI extended to a third dimension. Book XII ap-
plies the method of exhaustion to the measurement of circles,
spheres, pyramids, etc. Book XIII deals with regular solids.

Plato's fantastic speculations had raised the theory of
regular polyhedra to a high level of significance. Hence, a good
knowledge of the "Platonic bodies" 15 was considered by many
good people as the crown of geometry. Proclos (V-2) suggested
that Euclid was a Platonist and that he had built his geome-
trical monument for the purpose of explaining the Platonic
figures. That is obviously wrong. Euclid may have been a
Platonist, of course, but he may have preferred another phi-
losophy or he may have carefully avoided philosophical im-
plications. The theory of regular polyhedra is the natural
culmination of solid geometry and hence the Elements could
not but end with it.

It is not surprising, however, that the early geometers who
tried to continue the Euclidean efforts devoted special atten-
tion to the regular solids. Whatever Euclid may have thought
of these solids "beyond mathematics" they were, especially
for the neo-Platonists, the most fascinating items in geometry.
Thanks to them, geometry obtained a cosmical meaning and
a theological value.

Two more books dealing with the regular solids were added
to the Elements, called books XIV and XV and included in
many editions and translations, manuscript or printed. The
so-called "Book XIV" was composed by Hypsicles of Alex-
andria at the beginning of the second century B.C. and is a

15 For a discussion of the regular polyhedra and of the Platonic
aberrations relative to them, see my History of Science (1, 438-39) .

22

EUCLID AND HIS TIME

work of outstanding merit; the other treatise "Book XV" is of
a much later time and inferior in quality; it was written by a
pupil of Isidores of Miletos (the architect of Hagia Sophia,
c. 532) .

To return to Euclid and especially to his main work, the
thirteen books of the Elements, when judging him, we should
avoid two opposite mistakes which have been made repeatedly.
The first is to speak of him as if he were the originator, the
father of geometry. As I have already explained apropos of
Hippocrates, the so-called "father of medicine," there are no
unbegotten fathers except Our Father in heaven. If we take
Egyptian and Babylonian efforts into account, as we should,
Euclid's Elements is the climax of more than a thousand years.
One might object that Euclid deserves to be called the father
of geometry for another reason. Granted that many dis-
coveries were made before him, he was the first to build a
synthesis of all the knowledge obtained by others and himself
and to put all the known propositions in a strong logical order.
That statement is not absolutely true. Propositions had been
proved before Euclid and chains of propositions established;
moreover, "Elements" had been composed before him by Hip-
pocrates of Chios (V B.C.), by Leon (IV-1 B.C.), and finally
by Theudios of Magnesia (IV-2 B.C.). Theudios' treatise, with
which Euclid was certainly familiar, had been prepared for
the Academy, and it is probable that a similar one was in use
in the Lyceum. At any rate, Aristotle knew Eudoxos' theory
of proportion and the method of exhaustion, which Euclid
expanded in Books V, VI and XII of the Elements. In short,
whether you consider particular theorems or methods or the
arrangement of the Elements, Euclid was seldom a complete

25

ANCIENT SCIENCE AND MODERN CIVILIZATION

innovator; he did much better and on a larger scale what other
geometers had done before him.

The opposite mistake is to consider Euclid as a "textbook
maker" who invented nothing and simply put together in bet-
ter order the discoveries of other people. It is clear that a
schoolmaster preparing today an elementary book of geometry
can hardly be considered a creative mathematician; he is a
textbook maker (not a dishonorable calling, even if the pur-
pose is more often than not purely meretricious), but Euclid
was not.

A good many propositions in the Elements can be ascribed
to earlier geometers, but we may assume that those which
cannot be ascribed to others were discovered by Euclid him-
self; and their number is considerable. As to the arrangement,
it is sale to assume that it is to a large extent Euclid's own. He
created a monument which is as marvelous in its symmetry,
inner beauty and clearness as the Parthenon, but incomparably
more complex and more durable.

A full proof of this bold statement cannot be given in a
few paragraphs or in a few pages. To appreciate the richness
and greatness of the Elements one must study them in a well
annotated translation like Heath's. It is not possible to do
more, here and now, than emphasize a few points. Consider
Book I, explaining first principles, definitions, postulates, ax-
ioms, theorems and problems. It is possible to do better at
present, but it is almost unbelievable that anybody could have
done as well twenty-two centuries ago. The most amazing
part of Book I is Euclid's choice of postulates. Aristotle was,
of course, Euclid's teacher in such matters; he had devoted
much attention to mathematical principles, had shown the un-

24

EUCLID AND HIS TIME

avoidability of postulates and the need for reducing them to a
minimum; 16 yet, the choice of postulates was Euclid's.

In particular, the choice of postulate 5 is, perhaps, his
greatest achievement, the one which has done more than any
other to immortalize the word "Euclidean." Let us quote it
verbatim: 17

... if a straight line falling on two straight lines make the
interior angles on the same side less than two right angles,
the two straight lines if produced indefinitely meet on that
side on which the angles are less than two right angles."

A person of average intelligence would say that the pro-
position is evident and needs no proof; a better mathematician
would realize the need of a proof and attempt to give it; it
required extraordinary genius to realize that a proof was
needed yet imppssible. There was no way out, then, from
Euclid's point of view, but to accept it as a postulate and go
ahead.

The best way to measure Euclid's genius as evidenced by
this momentous decision is to examine the consequences of it.
The first consequence, as far as Euclid was immediately con-
cerned, was the admirable concatenation of his Elements. The
second was the endless attempts which mathematicians made
to correct him; the first to make them were Greeks, like
Ptolemy (II- 1) and Proclos (V-2) ; then Muslims, chiefly the
Persian, Nasir al-dln al-TusI (XIII-2), the Jew, Levi ben Ger-
son (XIV-1) , and finally "modern" mathematicians, like John

ia Aristotle's views can be read in Heath's Euclid (1, 117 ff., 1926) or in
his posthumous book, Mathematics in Aristotle (Oxford, Clarendon Press,
1949; Isis 41, 329).

17 For the Greek text and a much fuller discussion of it than can be
given here, see Heath's Euclid (1, 202-20). See also Roberto Bonola, Non-
Euclidean Geometry (Chicago, 1912; Horus 154).

25

ANCIENT SCIENCE AND MODERN CIVILIZATION

Wallis (1616-1703), the Jesuit father, Gerolamo Saccheri (1667-
1733) , of San Remo in his Euclides ab omni naevo vindicatus
(1733), the Swiss, 18 Johann Heinrich Lambert (1728-77), and
the Frenchman, Adrien Marie Legendre (1752-1833). The
list could be lengthened considerably, but these names suffice,
because they are the names of illustrious mathematicians repre-
senting many countries and many ages, down to the middle
of the last century. The third consequence is illustrated by the
list of alternatives to the fifth postulate. Some bright men
thought that they could rid themselves of the postulate and
succeeded in doing so, but at the cost of introducing another
one (explicit or implicit) equivalent to it. For example,

"If a straight line intersects one of two parallels, it will
intersect the other also." (Proclos)

"Given any figure there exists a figure similar to it of
any size." (John Wallis)

"Through a given point only one parallel can be drawn
to a given straight line." (John Playfair)

"There exists a triangle in which the sum of the three
angles is equal to two right angles." (Legendre)

"Given any three points not in a straight line there ex-
ists a circle passing through them." (Legendre)

"If I could prove that a rectilinear triangle is possible
the content of which is greater than any given area, I

would be in a position to prove perfectly rigorously the
whole of geometry." (Gauss, 1799).

All these men proved that the fifth postulate is not neces-
sary if one accepts another postulate rendering the same ser-

18 Yes, Swiss (Isis 40, 139).
26

EUCLID AND HIS TIME

vice. The acceptance of any of those alternatives (those
quoted above and many others) would, however, increase the
difficulty of geometrical teaching; the use of some of them
would seem very artificial and would discourage young stu-
dents. It is clear that a simple exposition is preferable to one
which is more difficult; the setting up of avoidable hurdles
would prove the teacher's cleverness and his lack of common
sense. Thanks to his genius, Euclid saw the necessity of this
postulate and selected intuitively the simplest form of it.
There were also many mathematicians who were so blind that
they rejected the fifth postulate without realizing that an-
other was taking its place. They kicked one postulate out of
the door and another came in through the window without
their being aware of it!

The fourth consequence, and the most remarkable, was
the creation of non-Euclidean geometries. The initiators have
already been named, Saccheri, Lambert, Gauss. Inasmuch as
the fifth postulate cannot be proved, we are not obliged to
accept it, and if so, let us deliberately reject it. The first to
build a new geometry on an opposite postulate was a Russian,
Nikolai Ivanovich Lobachevskii (1793-1850), who assumed
that through a given point more than one parallel can be
drawn to a given straight line or that the sum of the angles
of a triangle is less than two right angles. The discovery of a
non-Euclidean geometry was made at about the same time
by a Transylvanian, Janos Bolyai (1802-60). Sometime later,
another geometry was outlined by a German, Bernhard Rie-
mann (1826-66), who was not acquainted with the writings
of Lobachevskii and B61yai and made radically new assump-
tions. In Riemann's geometry, there are no parallel lines and
the sum of the angles of a triangle is greater than two right

27

ANCIENT SCIENCE AND MODERN CIVILIZATION

angles. The great mathematical teacher Felix Klein (1847-
1 925) showed the relationship of all those geometries. Euclid's
geometry refers to a surface of zero curvature, in between Rie-
mann's geometry on a surface of positive curvature (like the
sphere) and Lobachevskii's applying to a surface of negative
curvature. To put it more briefly, he called the Euclid geome-
try parabolic, because it is the limit of elliptic (Riemann's)
geometry on one side and of the hyperbolic (Lobachevskii's)
geometry on the other.

It would be foolish to give credit to Euclid for pan-
geometrical conceptions; the idea of a geometry different from
the common-sense one never occurred to his mind. Yet, when
he stated the fifth postulate, he stood at the parting of the ways.
His subconscious prescience is astounding. There is nothing
comparable to it in the whole history of science.

It would be unwise to claim too much for Euclid. The fact
that he put at the beginning of the Elements a relatively small
number of postulates is very remarkable, especially when one
considers the early date, say, 300 B.C., but he could not
fathom the depths of postulational thinking any more than he
could fathom those of non-Euclidian geometry. Yet he was
the distant forerunner of David Hilbert (1862-1911) even as he
was Lobachevskii's spiritual ancestor. 19

Enough has been said of Euclid the geometer, but one
must not overlook other aspects of his genius as mathematician
and physicist. To begin with, the Elements does not deal

19 For details, see Florian Cajori, History of Mathematics (2nd ed.,
326-28, 1919); Cassius Jackson Keyser, The Rational and the Superrational
(pp. 136-44, New York, Scripta Mathematica, 1952; Isis 44, 171) .

28

EUCLID AND HIS TIME

simply with geometry but also with algebra and the theory o
numbers.

Book II might be called a treatise on geometrical algebra.
Algebraical problems are stated in geometrical terms and
solved by geometrical methods. For example, the product of
two numbers a, b is represented by the rectangle whose sides
have the lengths a and b\ the extraction of a square root is
reduced to the finding of a square equal to a given rectangle,
etc. The distributive and commutative laws of algebra are
proved geometrically. Various identities, even complicated
ones, are presented by Euclid in a purely geometrical form.

or (a + b) 2 + (b - a) 2 = 2 (a 2 + 6 2 )

This might seem to be a step backward as compared with
the methods of Babylonian algebra, and one wonders how
that could happen. It is highly probable that the clumsy
symbolism of Greek numeration was the fundamental cause
of that regression; it was easier to handle lines than Greek
numbers!

At any rate, Babylonian algebraists were not acquainted
with irrational quantities, while Book X of the Elements (the
largest of the thirteen books, even larger than Book I) is de-
voted exclusively to them. Here again, Euclid was building
on older foundations, but this time the foundations were
purely Greek. We may believe the story ascribing recognition
of irrational quantitites to early Pythagoreans, and Plato's
friend Theaitetos (IV-1 B.C.) gave a comprehensive theory of
them as well as of the five regular solids. There is no better

29

ANCIENT SCIENCE AND MODERN CIVILIZATION

illustration of the Greek mathematical genius (as opposed tc
the Babyonian one) than the theory of irrationals as explained
by Hippasos of Mctapontion, Theodoros of Gyrene, Theaitetos
of Athens and finally by Euclid. 20 It is impossible to say just
how much of Book X was created by Theaitetos and how much
by Euclid himself. We have no choice but to consider that
book as an essential part of the Elements, irrespective of its
origin. It is divided into three parts, each of which is pre-
ceded by a group of definitions. A number of propositions
deal with surds in general, but the bulk of the book investi-
ga'es the complex irrationals which we would represent by the
symbols

V (Va V&)

wherein a and b are commensurable quantities. These irra-
tionals are divided into twenty-five species, each of which is
discussed separately. As Euclid did not use algebraical sym-
bols, he adopted geometrical representations for these quanti-
ties and his discussion of them was geometrical. Book X was
much admired, especially by Arabic mathematicians; it re-
mains a great achievement but is practically obsolete, for such
discussions are futile from the point of view of modern
algebra.

Books VII to IX of the Elements might be called the first
treatise on the theory of numbers, one of the most abstruse
branches of the mathematical tree. It would be impossible to
summarize their contents, for the summary would be almost

20 For Hippasos', Theodores', and Theaitetos' contributions see my
History of Science (pp. 282-85, 437) .

30

EUCLID AND HIS TIME

meaningless unless it covered a good many pages. 21 Let me
just say that Book VII begins with a list of twenty-two defini-
tions, which are comparable to the geometrical definitions
placed at the beginning of Book I. Euclid sets forth a series
of proportions concerning the divisibility of numbers, even and
odd numbers, squares and cubes, prime and perfect numbers,
etc.

Let us give two examples. In IX, 36 he proves that if
p=l + 2 + . . . -f 2 n is prime, 2 n p is perfect (that is, equal to
the sum of its divisors). In IX, 20 we are given an excellent
demonstration that the number of prime numbers is infinite.

The demonstration is so simple and our intuitive feeling
ad hoc so strong that one would readily accept other proposi-
tions of the same kind. For example, there are many prime
pairs, that is, prime numbers packed as closely as possible
(2n + 1, 2n + 3, both primes, e.g., 11, 13; 17, 19; 41, 43) . As
one proceeds in the series of numbers, prime pairs become
rarer and rarer, yet one can hardly escape the feeling that the
number of prime pairs is infinite. The proof of that is so
difficult, however, that it has not yet been completed. 22

In this field again, Euclid was an outstanding innovator,
and the few mathematicians of our own days who are trying
to cultivate it recognize him as their master.

21 The Greek text of Books VII to IX covers 116 pages in Heiberg's
edition (2, Leipzig, 1884) and the English translation with notes, J50 pages
in Heath's second volume.

32 Charles N. Moore offered a proof in 1944, but that proof was shown
to be insufficient (Horus 62). The incredible complexity of the theory of
numbers can be appreciated by looking at its History written by Leonard
Eugene Dickson (3 vols., Carnegie Institution, 1919-23; Isis 3, 446-48; 4,
107-08: 6, 96-98). For prime pairs, see Dickson, 7, 353, 425, 438.

31

ANCIENT SCIENCE AND MODERN CIVILIZATION

Thus far, we have spoken only of the Elements, but Euclid
wrote many other works, some of which are lost; these works
deal not only with geometry but also with astronomy, physics,
and music. The genuineness of some of those treatises is
doubtful. For example, two treatises on optics are ascribed to
him, the Optics and the Catoptrics. 23 The first is genuine, the
second probably apocryphal. We have the text of the Optics,
and we have also a review of both treatises by Theon of Alex-
andria (IV-2). The Optics begins with definitions or rather
assumptions, derived from the Pythagorean theory that the
r?ys of light are straight lines and proceed from the eye. Euclid
then explains problems of perspective. The Catoptrics deals
with mirrors and sets forth the law of reflection. It is a
remarkable chapter of mathematical physics which remained
almost alone of its kind for a very long period of time, but
does it date from the third century B.C., or is it later, much
later?

The tradition concerned with the fifth postulate has al-
ready been referred to; it can be traced from the time of the
Elements to our own. That is only a small part of it, however.
The Euclidean tradition, even if restricted to mathematics, is
remarkable for its continuity and the greatness of many of its
bearers. The ancient tradition includes such men as Pappos
(III-2) , Theon of Alexandria (IV-2) , Proclos (V-2), Marines of

" French translation by Paul Ver Eecke, l/Optitjiie ct la Catoptriqne
(Bruges, 1938; Isis 30, 520-21). This includes French versions of the
Catoptrics and of the two texts of the Optics, the original one and the
ene edited by Theon of Alexandria (IV-2). English translation of the
original text of the Optics by Harry Edwin Burton (Journal of the Optical
Society of America 3$ [1945], 357-72).

32

EUCLID AND HIS TIME

Sichem (V-2), Simplicios (VI- 1). It was wholly Greek. Some
Western scholars, such as Censorinus (1II-1) and Boethius

(VI- 1) , translated parts of the Elements from Greek into Latin,
but very little remains of their efforts and one cannot speak
of any complete translation, or of any one covering a large
part of the Elements. There is much worse to be said; various
manuscripts circulated in the West until as late as the twelfth
century which contained only the propositions of Euclid
without demonstrations. 24 The story was spread that Euclid
himself had given no proofs and that these had been supplied
only seven centuries later by Theon of Alexandria (1V-2). One
could not find a better example of incomprehension, for if
Euclid had not known the proofs of his theorems he would not
have been able to put them in a logical order. That order is
the very essence and the greatness of the Elements, but
medieval scholars did not see it, or at least did not see it until
their eyes had been opened by Muslim commentators.

The Muslim study of Euclid was begun by al-Kindi (IX- 1) ,
if not before (al-Kiridi's interest, however, was centered upon
the optics, and in mathematics it extended to non-Euclidean
topics such as Hindu numerals), and Muhammad ibn Musa

(IX- 1). The Elements were first translated into Arabic by
al-Hajjaj ibn Yusuf (IX- 1); he made a first translation for
Harun al-Rashid (caliph, 786-809), then revised it for al-
Ma'mun (caliph, 813-33) . During the 250 years which fol-
lowed, the Muslim mathematicians kept very close to Euclid,
the algebraist as well as the geometer, and published other
translations and many commentaries. Before the end of the
ninth century, Euclid was translated and discussed in Arabic

24 Greek and Latin editions of the propositions only, without proofs,
were printed from 1547 to as late as 1587.

33

ANCIENT SCIENCE AND MODERN CIVILIZATION

by al-Mahanl, al-Nairlzi, Thabit ibn Qurra, Ishaq ibn Hunain,
Qusta ibn Luqa. A great step forward was made in the first
quarter of the tenth century by Abu 'Uthman Sa'Id ibn
Ya'qub al-Dimishqi, who translated Book X with Pappos' com-
mentary (the Greek of which is lost) , 25 This translation in-
creased Arabic interest in the contents of Book X (classification
of incommensurable lines), as witnessed by the new translation

of Nazlf ibn Yumn (X-2), a Christian priest, and by the com-
mentaries of Abu Ja't'ar al-Khazin (X-2) and Muhammad ibn

'Abd al-Baqi al-Baghdadi (XI-2). My Arabic list is long yet
very incomplete, because we must assume that every Arabic
mathematician of this age was acquainted with the Elements
and discussed Euclid. For example, Abu-1-Wafa' (X-2) is said
to have written a commentary on Euclid which is lost.

We may now interrupt the Arabic story and return to the
West. Western efforts to translate the Elements directly from
Greek into Latin had been ineffective; it is probable that their
knowledge of Greek diminished and dwindled almost to noth-
ing at the very time when their interest in Euclid was in-
creasing. Translators from the Arabic were beginning to ap-
pear and these were bound to come across Euclidean manu-
scripts. Efforts to Latinize these were made by Hermann the
Dalmatian (XII-1), John O'Creat (XII-1) , and Gerard of
Cremona (XII-2) , but there is no reason to believe that the
translation was completed, except by Adelard of Bath (XII-
l). 26 However, the Latin climate was not so favorable to

25

The Arabic text of Abu 'Uthman was edited and Englished by Wil-
liam Thomson, with mathematical introduction by Gustav Junge (Harvard
Semitic Series 8, Cambridge, 1930; Isis 16, 132-36).

26 The story is simplified for the sake of brevity; for details, see Marshall
Clagett, "The medieval Latin translations from the Arabic of the Elements

34

EUCLID AND HIS TIME

geometrical research in the twelfth century as the Arabic cli-
mate had proved to be from the ninth century on. Indeed, we
have to wait until the beginning of the thirteenth century to
witness a Latin revival of the Euclidean genius, and we owe
that revival to Leonardo of Pisa (XI1I-1), better known under
the name of Fibonacci. In his Practica gcometriae, written in
1220, Fibonacci did not continue the Elements, however, but
another Euclidean work on the Divisions of figures, which is
lost. 27

In the meanwhile, the Hebrew tradition was begun by
Judah ben Solomon ha-Kohen (XIII-1) and continued by
Moses ibn Tibbon (XIII-2), Jacob ben Mahir ibn Tibbon
(XIII-2), and Levi ben Gerson (XIV-1) . The Syriac tradition
was illustrated by Abu-1-Faraj, called Barhebraeus (XIII-2),
who lectured on Euclid at the observatory of Maragha in 1268;
unfortunately, the beginning of the Syriac tradition was also
the end of it, because Abu-1-Faraj was the last Syriac writer
of importance; after his death, Syriac was gradually replaced
by Arabic.

The golden age of Arabic science was also on the wane,
though there remained a few illustrious Euclidians in the
thirteenth century, like Qaiar ibn abl-l-Qasim (XIII-1), Ibn
al-Lubudl (XIII-1), Nasjr al-dm al-Tusi (XIII-2), Muhylal-dm
al-Maghribi (XIII-2), Qutb al-din al-Shlrazi (XIII-2), and even
some in the fourteenth century. We may overlook the late Mus-

with special empasis on the versions of Adelard of Bath" (Isis 44, 16-42,
1953) .

27 The text of that little treatise peri diaireseon was restored as far as
possible by Raymond Clare Archibald on the basis of Leonardo's Practica
and of an Arabic translation (Intro, 1, 154-55).

35

ANCIENT SCIENCE AND MODERN CIVILIZATION

lim and Jewish mathematicians, however, for the main river
was now flowing in the West.

Adelard's Latin text was revised by Giovanni Campano
(XIII-2) and Campano's revision was immortalized in the
earliest printed edition of the Elements (Venice, 1482). The
first edition of the Greek text was printed in Basel, 1533, and
the princeps of the Arabic text, as edited by Nair al-dm al-
Tusi, was published in Rome in 1594.

The rest of the story need not be told here. The list of
Euclidean editions which began in 1482 and is not ended yet
is immense, and the history of the Euclidean tradition is an
essential part of the history of geometry.

As far as elementary geometry is concerned, the Elements of
Euclid is the only example of a textbook which has remained
serviceable until our own days. Twenty-two centuries of
changes, wars, revolutions, catastrophies of every kind, yet it
still is possible and profitable to study geometry in Euclid!

3. BIBLIOGRAPHY OF EUCLID

Standard edition of the Greek text of all the works, with
Latin versions, Euclidis opera omnia ediderunt J. L. Heiberg
et H. Menge (8 vols., Leipzig, 1883-1916; supplement 1899) .

Sir Thomas L. Heath. Euclid's Elements in English (3
vols., Cambridge, 1908), revised edition (3 vols., 1926; I sis 10,
60-62) .

Charles Thomas-Stanford. Early Editions of Euclid's Ele-
ments (64 pp., 13 pi., London, 1926; Isis 10, 59-60).

36

PTOLEMY AND HIS TIME

(second century A.D.)

1. THE LONG DURATION AND COMPLEXITY OF ANCIENT SCIENCE

i

.GNORANT people think of "antiquity" or of
the "Middle Ages" as if each of these periods were something
homogeneous and unchanging, and they would put everything
concerning ancient science (or medieval science) in a single
box, just as if all these things were of the selfsame kind. That
is very silly. The one thing which one might concede is that
the change is faster now than it was in the past, but much of
the increasing speed is superficial.

What we call classical antiquity, if we count it from Homer
to Damascios, is a period of about fourteen centuries; if we
count the length of American civilization in the same way

37

ANCIENT SCIENCE AND MODERN CIVILIZATION

(that is, leaving out, in both cases, the prehistoric times which
are ageless), it has lasted about four centuries. Thus, the first
of these periods is more than thrice longer than the second.
And yet should one put the whole of American culture in a
single bag, as if the whole of it were the same kind of biscuit?
Certainly not.

There was incredible variety in ancient times, even within
a single century, but there were also traditions which continued
across the ages and are very helpful to us as guiding threads.
For example, from Euclid's time on, there appeared in each
century some mathematicians who continued Euclid's ideas
or discussed them.

By the second century after Christ more than three cen-
turies had elapsed since the beginning of the Hellenistic Age,
and the world was exceedingly different from what it had been.
The dilfercnce was not due so much to Christianity, which was
still unfelt except by a small minority of people, and re-
mained inoperative as an influence. The philosophical climate
continued to be dominated by Stoicism. The political world,
however, was absolutely different.

2. THE ROMAN WORLD IN THE SECOND CENTURY

Let us consider a little more closely the world in which
Ptolemy lived. It is probable that he was born in Egypt and
flourished in Alexandria, but Egypt had been a Roman pro-
vince since 30 B.C. The Greek chaos and the wars between
Alexander's successors had been finally ended by Roman
power. That new world was very imperfect in many ways
but, for the first time in many centuries, there was a modicum
of international order, law and peace. The second century was
the end of the golden age of the Roman empire; it was de-

38

PTOLEMY AND HIS TIME

cidedly the golden age of Roman science, but the best of
Roman science was really Greek.

It was Ptolemy's privilege to live under some of the best
emperors, the Spaniard Trajan (ruled 98-1 17), who built roads,
libraries, bridges across the Danube and the Tagus; Hadrian
(ruled 117-38), also a great builder in Athens, Rome and
Tivoli; Antoninus Pius (ruled 138-61) and, perhaps, Marcus
Aurelius (ruled 161-80) ; these last two, not only great em-
perors, but good men. When one speaks of "pax romana," one
has in mind chiefly the forty-four years covered by the rules
of Hadrian and Antoninus, and apropos of the rules of
Antoninus and Marcus Aureiius, a stretch of almost equal
duration, Gibbon declared: "Their united reigns are possibly
the only period of history in which the happiness of a gieat
people was the sole object of government." 1

The most significant thing about the Roman empire, from
the intellectual point of view, was its bilingualism. Every
educated man in the West was supposed to know two langu-
ages, Greek as well as Latin. By this time, the second century
after Christ, the golden age of Latin literature was already
past and yet the top culture of the West was Greek, not Latin.
Greek was the language of science and philosophy; Latin the
language of law, administration and business. Hadrian knew
Greek very well and had created in Rome a college of arts
which was called Athenaeum, 2 in honor of the goddess,

1 Decline and Fall, chap. 3. In Bury's illustrated edition, 1, 84.

2 The name Athenaeum has become a common name in almost every
European language. Every government high school in Belgium is called
athene'e. In English and other languages the word is used to designate
a literary or scientific association or club. It is one of the words which
remind us every day of our debt to antiquity, the others being academy,
lyceum, museum.

39

ANCIENT SCIENCE AND MODERN CIVILIZATION

Athene, the city of Athens (which Hadrian loved) and Greek
culture. Marcus Aurelius wrote his famous Meditations in
Greek. In spite of the prestige attained by such writers as
Lucretius, Cicero, Virgil and Seneca, and of the scientific books
written in Latin by Vitruvius, Celsus, Frontinus and Pliny, the
language of science was still predominantly Greek. It is true
that the two greatest scientists of the age were born in the
Orient, Ptolemy in Egypt and Galen in the province of Asia,
and neither of them would have been able to write in Latin,
even if they had wished to do so. But why should anyone
write artificially in an inferior language, if he was able to
write naturally in a superior one?

Any Roman of the second century who was intellectually
ambitious had to learn Greek; the result was obtained chiefly
with the help of Greek tutors or by years of "graduate study"
in Athens, Alexandria or any other city in the eastern pro-
vinces. The situation can be compared to another closer to
us. When Frederick the Great was king of Prussia (1740-86),
he would speak German to his soldiers or servants, but French
was the language of polite conversation; memoirs sent to the
Berlin Academy had to be written in French or Latin, not in
German, to be published.

The world in which Ptolemy lived was a Roman world,
whose intellectual ideas were still predominantly Greek.

3. PTOLEMY AND HIPPARCHOS

The two outsanding men of science of the second century
were Ptolemy, in the first half, and Galen in the second. They
were two giants of the most genuine kind; the kind of giants
who do not become smaller as the centuries pass but greater
and greater. One cannot consider Ptolemy without evoking

40

PTOLEMY AND HIS TIME

his predecessor, Hipparchos of Nicaia, who flourished in the
Hellenistic Age, 3 almost three centuries before him. It is
strange to think of two men separated by so large a barrier-
three centuriesyet working as if the second were the im-
mediate disciple of the first.

Hipparchos' works are lost, and it is possible that their
loss was partly the result of the fact that Ptolemy's great book
superseded them and made them superfluous. In some in-
stances, Ptolemy's debt to his predecessor is acknowledged or
is made clear in other ways. What we know of Hipparchos we
know almost exclusively from Ptolemy, who quotes him often,
sometimes verbatim. 4 Nevertheless, in the majority of cases, it
is impossible to say whether the real inventor was the older
or the younger man.

In what follows we shall not bother too much about that,
and Ptolemy's achievements will be described as if they were
exclusively or mainly his own. After all, that is the method
which one cannot help following in discussing the achieve-
ments of almost any ancient scientist.

Euclid is mainly known as a mathematician, and his fame
is based upon the Elements; Ptolemy's personality was far
more complex and two of his books, the Almagest and the
Geography, remained standard textbooks in their fields for at
least fourteen centuries.

The comparison of Ptolemy with Euclid is a very useful
one, because the fact that their books superseded earlier ones
was essentially due to the same causes. Ptolemy, like Euclid,

8 Hipparchos flourished in Rhodes from 146 to 127 and perhaps also
from 161 to 146 in Alexandria.

4 See the index nominum in Heiberg's edition (1907) , 3 (called II),
pp. 275-77.

41

ANCIENT SCIENCE AND MODERN CIVILIZATION

was an excellent expositor or teacher; while their predecessors
had written monographs or short treatises, they wrote very
large ones of encyclopaedic nature and did it in the best order
and with perfect lucidity. Both men combined an extra-
ordinary power of synthesis and exposition with genius of the
highest potential. The earlier treatises which had been the
foundation of their own were soon judged to be incomplete
and obsolete and the scribes ceased to copy them; thus, they
were not only superseded but dropped out of existence.

4. PTOLEMY'S LIFE

It is tempting to compare Ptolemy with Euclid, two giants
who shared the distinction of composing textbooks which
would remain standard books in their respective fields for
more than a thousand years. They are singularly alike in their
greatness and in their loneliness. We know their works ex-
ceedingly well, but they themselves are practically unknown.

Ptolemy's biography is as empty as Euclid's. We do not
even know when and where he was born and died. It has
been said, very late (fourteenth century) that he was born in
Ptolemai's Hermeiu, a Greek city of the Thebais. 5 That is
possible. He was probably a Greek Egyptian or an Egyptian
Greek; he made astronomical observations in Alexandria or
in Canopos nearby from 127 to 151 (or 141?); according to
an Arabic story, he lived to be seventy-eight; according to Suidas
(X-2), he was still alive under Marcus Aurelius (emperor 161-
80); we may conclude that he was probably born at the end of
the first century.

B Upper Egypt, he ano chora. Ptolemais Hermeiu was on the site of
the Egyptian village al-Minshah.

42

PTOLEMY AND HIS TIME

As to his character, we have a glimpse of it in the Prooimion

(or preface) to the Almagest, addressed to his friend Syros. 6

That preface is a noble defense of mathematics and especially

of celestial mechanics. Another glimpse, indirect, is given in

an early epigram:

I know that I am mortal and ephemeral, but when 1
scan the crowded circling spirals of the stars 1 do no longer
touch the earth with my feet, but side by side with Zeus I
take my fill of ambrosia, the food of the gods.

This epigram is included in the Greek Anthology (IX,
577) , bearing Ptolemy's name; this does not prove Ptolemy's
authorship but is a good witness of him, like a portrait. The
poet saw him as a man lifted up far above other men by his
lofty purpose and equanimity.

5. THE ALMAGEST

Out of many books of his, and of his two great classics,
the best known is the Almagest. Its curious name will be ex-
plained later when we discuss the Ptolemaic tradition. At pre-
sent, let us take it for granted as most people do. The original
Greek title he tnathcmatike syntaxis means the Mathematical
Synthesis. It was really a treatise of astronomy but astronomy
was then a branch of mathematics; one is reminded of another
classic which was published more than eighteen centuries later,
Newton's Mathematical Principles of Natural Philosophy.

Ptolemy's astronomy, like Hipparchos', was based upon
observations, his own and those of Greek and Babylonian pre-

a Syros, otherwise unknown, must have been a very good friend of
Ptolemy, for the latter appeals to him thrice, "o Syre," at the beginnings
of Books I and VII and at the end of Book XIII; that is the beginning,
the middle and the very end of the Almagest.

43

ANCIENT SCIENCE AND MODERN CIVILIZATION

decessors. Hipparchos had used various instruments, e.g., a
celestial sphere and an improved diopter, and Ptolemy had
perhaps added new instruments or improved the older ones.
In this case, as in most cases, it is impossible to separate the
achievements of both men and to say whether the meridian
circle, the astrolabon organon, the parallactic instrument and
the mural quadrant were invented by Ptolemy or improved
by him or completely invented by Hipparchos. The history
of instruments, we should remember, is one of the best ap-
proaches to the understanding of scientific progress, but it is
full of difficulties; each instrument is developed gradually;
none is created in one time for all time by a single man. 7 Their
main task, however, as they undersood it, was not so much
the taking and recording of observations, but the mathematical
explanation of the facts which those observations revealed,
and their synthesis. Therefore, the Almagest of Ptolemy, like
the Principia of Newton, was primarily a mathematical book
and its original title, Mathematical Syntaxis, was adequate.

The Almagest is divided into thirteen books. The first two
are introductory, explaining astronomical assumptions and
mathematical methods. Ptolemy proves the sphericity of the
Earth and postulates the sphericity of the heavens and their
revolution around the Earth immobile in the center. He dis-
cusses and redetermines the obliquity of the ecliptic. The main
mathematical method is trigonometry, for Ptolemy realized
that spherical geometry and graphical means were incon-
venient and insufficient. In this he was not independent of

7 For general considerations on instruments, see Maurice Daumas, Les
instruments scientifiques aux XVII* et XVIHe sitcles (Paris, 1953: Isis 44,
391). Daumas deals with late instruments, but many of his remarks apply
just as well to the ancient ones.

44

PTOLEMY AND HIS TIME

Hipparchos but, in addition, he was privileged to stand upon
the shoulders of Menelaos of Alexandria.

The trigonometry is explained in chapters numbered 11
and 13 in Heiberg's edition. Every distance on the sphere is
an angular one; the measurement of angles is replaced by the
consideration of the chords subtending the corresponding
arcs. 8 The circle is divided into 360 and the diameter into
120 parts. Ptolemy used sexagesimal numbers in order to
avoid the embarrassment of fractions (that is the way he put
it, Almagest I, 10). Thus, each of the 60 parts of the radius
was divided into sixty small parts, and these again were
divided into sixty smaller ones. 9 A table of chords was com-
puted for every half degree, from to ISO , 10 each chord be-
ing expressed in parts of the radius, minutes and seconds. The
size of some chords (sides of regular polygons) could be de-
rived easily from Euclid; the size of others was obtained, thanks

8 Later on, Arabic astronomers inspired by Hindu ones replaced the
chords by sines and other ratios, but the purpose of Ptolemaic (Hipp-
archian) trigonometry was the same as ours. Assuming the radius to be
the unit,

chord a = 2 sin (a/2)
sin a (i/ 2 ) chord (2a) .

9 In Latin, the small parts were called partes minutae primae, and the
smaller ones, partes minutae secundae. Our words minutes and seconds
were stupidly derived from the first adjective in the first expression and
from the second in the second.

10 Ptolemy's table of chords, as given in the Almagest (I, 11), is thus
like a table of sines for every quarter degree from 1 to 90. The sines
which could be obtained from his table would be correct to 5 places. The
table allowed him to determine pi with remarkable precision. Let us
assume that the length of the circumference is very close to 360 times the
chord of 1, each of which measures 1 part 2'50". Pi is the ratio of ihe
circumference to the diameter, or 360/120 (1 part 2'50") = 3 parts 8'30"
= 3.14166 (real value 3.14159...).

45

ANCIENT SCIENCE AND MODERN CIVILIZATION

to Ptolemy's theorem about quadrilaterals inscribed in a circle;
that theorem enabled one to find the chord of a sum of angles.
Opposite the value of each chord in the table is given 1/30 of
the excess of that chord over the preceding one; this 1/30 is
expressed in minutes, seconds and thirds; this would enable
one to compute the chords for every minute of angle. Ptolemy
understood the meaning of interpolations and approximations;
his correct appreciation of them was one of the bases of applied
mathematics.

The table of chords is followed by a geometrical argument
leading to the calculation of the relations of arcs of the equa-
tor, ecliptic, horizon and meridian, and tables ad hoc. The
same kind of discussion is continued in Book II with reference
to the length of the longest day at a given latitude.

Book III deals with the length of the year and the motion
of the Sun, Ptolemy using epicycles and eccentrics (the first of
which certainly and the second probably invented by Apol-
lonios of Perga, II 1-2 B.C.) .

Book IV. Length of the month and theory of the Moon.
This contained what is supposed to be one of his discoveries
(as distinguished from those of Hipparchos), the second in-
equality of the Moon called evection. He fixed the amount of
it at 119'30", and accounted for it in terms of eccentrics and
epicycles and of a small oscillation (prosneusis) of the epicycle.
This is a good example of mathematical ingenuity. 11

Book V. Construction of the astrolabe. Theory of the Moon

11 The evection, caused by the Sun's attraction, depends upon the

alternate increase and decrease of the eccentricity of the Moon's orbit;

the eccentricity is maximum when the Sun is crossing the line of the apses

(syzygies) and minimum at the quadratures. The value of the evection

is about 1 15', and its period, about li/& year.

46

PTOLEMY AND HIS TIME

ontinued. Diameters of the Sun, Moon, Earth's shadow, dis-
ance of the Sun, dimensions of the Sun, Moon and Earth.

Book VI. Solar and lunar eclipses.

Book VII- VIII. Stars. Precession of the equinoxes. The
able of stars covers the end of VII and the beginning of VIII.
The rest of VIII describes the Milky Way and the construction
>f a celestial globe.

Books IX-XIII. Planetary motions. This is perhaps the
nost original part of the Almagest, because Hipparchos had
lot been able to complete his own synthesis of planetary sys-
ems. Book IX deals with generalities, such as the order of the
>lanets according to their distances from the Earth and periods
>f revolution; then with Mercury. Book X Venus; XI Jupiter
nd Saturn; XII Stationary points and retrogressions, greatest
longations of Mercury and Venus; XIII Motions of planets
n latitude, inclinations and magnitudes of their orbits.

In short, the Almagest was a survey of the astronomical
Lnowledge available about 150 A.D., and that knowledge was
lot essentially different from that attained in 150 B.C. It is
mpossible to discuss the details of it without discussing the
vhole of ancient astronomy. Let us consider a few points.

First the Almagest defined what we call the "Ptolemaic
ystem," that is, the solar system centered upon the Earth.
Allowing Hipparchos, Ptolemy rejected the ideas of Arist-
irchos of Samos (III-l B.C.) , who had anticipated the Coper-
lican system; Hipparchos and Ptolemy rejected those ideas 12
>ecause they did not tally sufficiently well with the observa-
ions. Their objections were of the same nature as Tycho

12 They even rejected the geoheliocentric system of Heracleids of
'ontos (IV-2 B.C.). The Ptolemaic system was completely geocentrical.

47

ANCIENT SCIENCE AND MODERN CIVILIZATION

Brahc's at the end of the sixteenth century; a sufficient agree-
ment between observations and the Aristarchian or Copernican
ideas became possible only when Kepler replaced circular
trajectories by elliptic ones (1609). The methodic excellence
of the Almagest caused the supremacy of the Ptolemaic system
until the sixteenth century, in spite of abundant criticisms
which became more and more acute as observations increased
in number and precision.

One might say that Hipparchos and Ptolemy were back-
ward in two respects, because they rejected the heliocentrical
Ideas of Aristarchos and the ellipses of Apollonios, but such
a conclusion would be very unfair. Men of science are not
prophets; they see a little further than other men but can
never completely shake off the prejudices of their own en-
vironment. As heliocentricity did not lead to greater simplicity
or precision, their rejection of it was justified.

The Catalogue of Stars is the earliest catalogue which has
come down to us. It includes 1,028 stars and gives the longi-
tude, latitude and magnitude of each. It was largely derived
from Hipparchos' 13 catalogue of c. 130 B.C.; Ptolemy left the
latitudes unchanged but added 240' to every longitude in
order to take the precession into account. The precession of
the equinoxes had been discovered by Hipparchos on the basis
of earlier observations, Babylonian and Greek. The precession
amounts to little more than one degree per century; 14 con-

18 Hipparchos had listed not many more than 850 stars giving the
latitude, longitude and magnitude of each.

14 Hipparchos assumed that the precession amounted to 45" or 46"
a year, which would add up to l.3 in a century; Ptolemy corrected that
to 36", which is exactly 1 a century. The real value is 50."25, equivalent
to l.4 a century. Hipparchos was closer to the truth than Ptolemy.

48

PTOLEMY AND HIS TIME

sidering the observational means of the ancient astronomers,
it is clear that they could not discover it without the knowledge
of stellar longitudes antedating their own by many centuries.

Before abandoning Ptolemaic astronomy, a few words
must be said of the methods of projection, orthographic and
stereographic, in spite of the fact that they are not explained
in the Almagest but in separate monographs. 15 It is possible
that both methods were invented by Hipparchos; at any rate,
Ptolemy's explanation of them is the earliest available.

Both methods were needed to solve a fundamental problem,
the representation of points or arcs of the spherical surface
of heaven 16 upon a plane (or map) . In the Analemma
method, the points and arcs were projected orthogonally
upon three planes mutually at right angles, the meridian,
hori/on and prime vertical; this method was used chiefly to
find the position of the Sun at a given hour. The method of
the Planisphaerium was what is now called stereographic pro-
jection. Every point of the sphere is represented by its pro-
jection upon the equator from the opposite pole (the northern
hemisphere was projected by Ptolemy from the south pole).
This particular system of projection had very remarkable and
useful properties, of which Ptolemy was aware though he did

15

The orthogonal projection is explained in the Analemma (meaning
taking-up, Aufnahme, also sundial), and the stereographic in the Plani-
sphaerium, both lost in Greek but preserved in Latin translations from
the Arabic. Latest editions, by J. L. Heiberg, in the Ptolemaei Opera (2,
187-223, 225-59, 1907). The second was translated into German by }.
Drecker (Isis 9, 255-78, 1927), who summarized the tradition of the
Planisphaerium in his preface.

16 All the stars and planets were supposed, for geometrical purposes, to
move on a single sphere. That was all right; if a star was not on the
sphere, its central projection on it was considered; the angular distances
remained the same.

49

ANCIENT SCIENCE AND MODERN CIVILIZATION

not give general proofs of them. The projection of all circles
are circles (with the apparent exception of circles passing
through the pole which are projected as straight lines). The
stereographic projection is the only one which is both con-
formal and perspective, 17 Ptolemy could not have known that
unicity, but he had made a good study of projections and was
lucky.

6. THE GEOGRAPHY

Ptolemy's geographical treatise or guide (geographice
hyphegesis) is almost as important as the Almagest. It covered
the whole of mathematical geography, just as the Almagest
covered the whole of mathematical astronomy, and it in-
fluenced geography as deeply and as long as the Almagest in-
fluenced astronomy. During fourteen centuries, at least, the
Almagest was the standard book, or call it the Bible, of
astronomy, while the Geography was the Bible of geography.
The name Ptolemy meant geography to geographers and
astronomy to astronomers.

The Geography was composed after the Almagest, say, after
150. It was divided into eight books and was restricted to
mathematical geography and to all the information needed for
the drawing of accurate maps. His knowledge was derived
mainly from Eratosthenes, Hipparchos, Strabon (1-2 B.C.), and,
above all, from Marinos of Tyre (II- 1), whom he praised yet
criticized.

17 A conformal projection is one in which the angles between two in-
tersected curves are the same in projection. A perspective projection is one
in which there is a 1 to 1 correspondence between any point on the sphere
and its projection on the plane.

The first to prove that the stereograph ical projections of spherical
circles are circles was Jordanus Nemorarius (XIII- 1).

50

PTOLEMY AND HIS TIME

We know Marines only through Ptolemy, who paid a very
moving tribute to him in chapter 5 of Book I and referred to
him many times; we may be sure that he quoted Marines
fairly, even when he disagreed with him. The relationship of
Ptolemy to Marinos is very much like his relationship to
Hipparchos, the great difference being that Marinos flourished
not Jong before Ptolemy, 18 while Hipparchos was three cen-
turies distant.

Ptolemy put together the geographical contributions of
his predecessors and his own and thus created the first general
treatise on geography. He was not interested in physical and
human geography as Strabon and Pliny were, and it is not fair
to reproach him for not having dealt with subjects which
did not concern him.

Book I discusses generalities, the size of the Earth and of
the known world, methods of cartographic projection, etc.
Books II to VII are systematic descriptions of the world in the
form of tables giving the longitudes and latitudes of places,
for every country of which he had sufficient knowledge.
Ptolemy (or Marinos) was the first to speak of longitudes
and latitudes (mecos, platos) as we do, meaning the distance
in longitude or latitude to a zero circle. Some 8,000 places,
"remarkable cities" (poleis episemoi), rivers, etc., are listed.
The identification of many of those places is very difficult, if
not impossible, in spite of abundant investigations by scholars
very familiar with the regions concerned. The world which he
tried to describe extended roughly from 20 S to 65 N and

18

Ptolemy called him (Geography 1, 6) "the latest of our age"
(hystatos te ton cath' hemas) which is not quite clear; he does not say
that he knew him personally. Hence, Marinos was a late predecessor,
how late? Hipparchos was also, in some respects, a late predecessor.

51

ANCIENT SCIENCE AND MODERN CIVILIZATION

from the Canary Islands at the extreme west to some 180
eastward from them. The tables made it possible to draw
maps wherein every item would be placed at its proper latitude
and longitude; such maps were probably included in the proto-
type manuscripts, because there are definite references to them
in Book VIII, which is a kind of astronomical epilogue. The
earliest manuscripts that have come to us are considerably
later, say, thirteenth century, but may represent a tradition
going back to Ptolemy and Marinos.

Ptolemy's intentions were excellent, but their realization
very imperfect. He was right in believing that in order to pro-
duce an accurate map, one must first prepare a net of meridians
and parallels, and his method of projection was distinctly
superior to Marinos'. When the net is ready, one may easily
mark upon it as many places as possible, the coordinates of
which are known. So far so good, but the map will be true
only if those coordinates have been established by astrono-
mical methods. Unfortunately, very few latitudes were cor-
rectly determined and no longitudes at all (the means were
lacking). His coordinates were computed on the basis of dead
reckonings, itineraries, traveller's tales and very few scientific
observations. His theory of projection was very much better
than the data to be projectedl The net itself was insufficient,
because his estimate of the Earth's size was inaccurate and be-
cause his first meridian was wobbly.

The central degree of latitude was our 36 (Gibraltar,
Rhodos) and that was convenient. The prime meridian was
drawn through the Fortunate Islands (Canaries plus Madeiras);
thus all the longitudes would extend only on the east side of 0.
Unfortunately, the relationship of that first meridian to the

52

PTOLEMY AND HIS TIME

continent was very inaccurate. As to the size of the Earth,
Ptolemy had preferred the estimate of Poseidonios (1-1 B.C.)
to that far more correct one of Eratosthenes (III-2 B.C.). 19 His
estimate of the length of the Eurasian continent was much
exaggerated, 180 instead of 130. This would eventually in-
crease the hopes of Columbus and early circumnavigators but
was poor geography.

There is not much point in criticizing his views of the
unknown part of the world, for such views could only be worth-
less guesses. For example, his rejection of the circumambient
ocean 20 was not more arbitrary than its acceptance by earlier
geographers.

The tradition of every Greek text is open to doubts be-
cause the earliest manuscripts that have come down to us are
always many centuries late. In the case of the Geography, the
difficulties are much increased by the necessity of considering
two traditions which may have concurred or not, the literary
tradition and the cartographic one. I am willing to accept the
conclusions of one of the greatest scholars, Father Joseph
Fischer, S. J., 21 who devoted the best part of his life to that
subject that the maps which have come down to us in the
earliest manuscripts (none earlier than the thirteenth century,

19 According to Eratosthenes, the circumference of the Earth was 252,-
000 stadia; according to Poseidonios, 180,000 stadia. This might be the
same measurement, if the stadia used in both cases were in the ratio
20/21. If Eratosthenes' stadia were 10 to a mile, then his measurement
equalled 37,495 km. (close to the real value 40,120 km.). For details, see
Aubrey Diller, "Ancient Measurements of the Earth" (Isis 40 [1949], 6-9) .

20 The Homeric views of the circumambient ocean were probably of
Phoenician origin. However far the Phoenicians might sail, they were
always stopped by the ocean. Herodotos was alone in his scepticism about
it (History of Science, pp. 138, 186, 310, 510, 526).

81 Joseph Fischer, S. J. (1858-1944). See Isis (37, 183).

53

ANCIENT SCIENCE AND MODERN CIVILIZATION

eleven centuries later than the lost prototypes) go back, even
as the text, to Ptolemy or even to Marines (it is hardly pos-
sible to distinguish between these two). The production of a
world map was Ptolemy's definite aim; 22 he may have failed to
produce it himself, and later maps, by Agathodaimon of
Alexandria or others, may have been graphical representations
of the tables. Certain knowledge is out of the question, but
I prefer to share Father Fischer's confidence than Bagrow's
hypercriticism. 23

On the Ptolemaic maps, meridians are drawn for every
5 and marked so in the margin, but parallels are established
according to the length of the longest day (for every quarter-
hour difference). In the Geography (I, 23), there is a table
giving lengths of day with corresponding latitudes. 24 This
part of the tradition goes back to the Eratosthenian concept of
climata: zones of the Earth's surface at such a distance from
each other that the average length of the longest day differs
by half an hour from the one to the other. There were seven
such climata, because there was no room for more in the
known world, ranging from a longest day of thirteen hours in

23 Geography (1,2, 2). Text quoted in Greek and Latin in Isis (20, 269).
28 Leo Bagrow, The Origin of Ptolemy's Geographia (Stockholm, 1046;

Isis 37, 187) . According to Bagrow, the text of the Geography is a late
Byzantine compilation (say, tenth or eleventh century) and the maps, as
we have them, are later than the text, say, thirteenth century. Such claims
can be neither proved nor disproved.

24 There is a similar table in the Almagest (XII, 6) wherein the lati-
tudes are expressed with more precision in degrees and minutes. In the
Geography, they are expressed in degrees and Egyptian fractions. Thus,
to 13 hours correspond in the Almagest lat. 1627', in the Geography
16 1/3 1/12 (=1625'). Aubrey Diller, "The Parallels on Ptolemaic
Maps" (Isis 33, 5-7, 19*t).

54 .

PTOLEMY AND HIS TIME

Meroe (in Nubia, lat. 17 N) to one of sixteen hours at the
Borysthenes (Dnieper).

Ptolemy was aware of the imperfection of his knowledge
and of the indetermination of his data, but the tabular form
obliging him to state for each place definite latitudes and
longitudes gave an impression of far greater exactness than
was warranted, and his followers' assumption of the correctness
of those numbers was the cause of many errors.

The knowledge of the world revealed in the Geography is
often inaccurate, but its extent and diversity are, nevertheless,
astonishing. Consider, for example, the data relative to equa-
torial Africa, the Upper Nile and the equatorial mountains
(Lunae Mons, Geography IV, 8) . This is the more remark-
able, if one bears in mind the confusion of ideas which still
obtained as late as the third quarter of the last century. 25

7. PTOLEMY'S OPTICS

In speaking of Euclid's Optics I remarked that he dealt
with a few phenomena in a geometrical way. Two optical
treatises are ascribed to Ptolemy; one, entitled in Latin Pto-
lomei de speculis, has been restituted to Heron of Alexandria,
who flourished possibly before Ptolemy; the other, called
Ptolemy's Optics, has come down to us in a Latin version
made from the Arabic in 1154 by Eugene of Palermo (XII-2). 26

This second treatise, the only one which we need consider
here, is divided into five books, but Book I and the end of

86 Intro. (3, 1158-60).

26 Heron, wrongly placed in my Introduction (/, 208), flourished after
62 and before 150 (Isis 30, 140; 32, 263-66). Latin-German edition of De
speculis by Wilhelm Schmidt (Heronis opera, 2, 301-65, 1900). Gilberto
Govi, L'ottica di Tolomeo de Eugenio (Torino, 1885) . Lejeune is prepar-
ing a new edition of this text.

55

ANCIENT SCIENCE AND MODERN CIVILIZATION

Book V arc lost. Such as it has come to us, it is very different
from Euclid's work, being physical and even psychological, for
Ptolemy tried to explain vision in concrete sensual terms. His
effort was understandable but premature, for the anatomical
and physiological knowledge of the eye was still utterly in-
sufficient. 27

Books III and IV deal with catoptrics and constitute the
most elaborate study of mirrors which has come down to us
from antiquity. Book V deals with refraction and includes
a table of refraction from air to water which is remarkable
enough to be reproduced here. 28

first real

i r difference value of r error

10

8

728'

+32'

730'

20

1530'

1451'

+39'

7

30

2230'

22T

+29'

6 30'

40

29

2849'

+11'

6

50

35

353'

3'

530'

60

4030'

4030'

5

70

4530'

4448'

+42'

4 30'

80

50

4736'

+224'

27 Albert Lejeune, "Les tables de retraction de Ptolme" (Annales de
la Societe scientifique de Bruxelles 60 [1946], 93-101) ; "Les lois de la
reflection dans 1'Optique de Ptolemee" (L'antiquite classique 15 [1947],
241-56; Isis 39, 244); Euclide et Ptolemee. Deux stades de I'optique
geometrique grecque (Louvain, 1948) , Isis 40, 278).

* 8 Figures as given by Lejeune, 1946 (p. 94).

56

PTOLEMY AND HIS TIME

That table is unique in classical literature, and it astonished
historians of physics so much that they took it too readily at
its face value. Ptolemy's study of refraction was spoken of as
the most remarkable experimental research of antiquity. I am
sorry to have to confess that I helped to diffuse that judg-
ment, 29 which has proved since to be erroneous; or, to put it
otherwise, Ptolemy's results are still very remarkable but in an
unexpected way.

Looking at the first differences in column 3, one im-
mediately sees that they form an arithmetical series, the differ-
ence between two successive terms being i/g . Now, can that be
the result of observations? (Note the observational errors in
the last column.) It is certain that Ptolemy made some ob-
servations with care; he did not continue them, however, but
generalized them prematurely, and built his table a priori.
Lejeune has suggested that he may have been misled by early
Greek authorities or by Babylonian examples. Constancy of
second differences may be noticed in polygonal numbers and
some tables of the Sun show that Chaldean astronomers had
tried to account for the Sun's irregular speed by constant
second differences.

The ancients did not yet understand the supremacy of ob-
servations as we do and used observational results rather as
indicators justifying the formulation of a theory, even as guide-
posts help travellers to find the right path. Before judging
them too severely, we should remember that their observational
means were generally so poor that the results of observations
could not possibly have with them the same authority as
they have with us.

29 Intro. (1,274).

57

ANCIENT SCIENCE AND MODERN CIVILIZATION

As Ptolemy was unfamiliar with sines, one could not expect
him to discover the law of refraction, 30 but it is interesting to
examine his results from that hindsight point of view. Let us
call the angles of incidence and refraction enumerated in his
table a and b. The average ratio sin a/sin b is 1.311, with an
average error of 0.043; the ratio a/b, however, is 1.42 with an
average error of 0.044. 31 Hence, Ptolemy's results, as given in
his table, would not have enabled him to find the constancy
of sin a/sin b; that is, he would have risked, instead, finding
tne constancy of a/b; he would have found a wrong law in-
stead of the true one.

At any rate, Ptolemy understood very clearly the fact that
a ray of light is deviated when it passes from one medium into
another of different density (as we would put it), and he ex-
plained the error caused by refraction in astronomical observa-
tions. It is disturbing, however, to find no mention of atmos-
pheric refraction in the Almagest; we must conclude that the
Optics was written by Ptolemy after the Almagest^ 2 or that it
was written by somebody else. The subject was not tackled
again until much later, by Ibn al-Haitham (XI-1); for the first
accurate determinations one had to wait until Tycho Brahe

80 The law was discovered by Willebrord Snel in 1618; published again
by Descartes in 1637.

81 The figures quoted are taken from Ernst Gerland, Geschichte der
Physik (p. 124, Miinchen, 1913; Isis 1, 527-29).

82 1 prefer the first hypothesis. Having discovered refraction, Ptolemy
could conceive the idea of atmospheric refraction. This is maximum at the
horizon (almost 35') and creates phenomena (e.g., at sunset or sunrise)
which must or may puzzle the intelligent observer. A knowledge of re-
fraction (cataclasis) , even atmospheric refraction, is ascribed also to
Cleomedes, who may be posterior to Ptolemy, in spite of my having classi-
fied him tentatively under (1-1 B.C.).

58

PTOLEMY AND HIS TIME

(1580), Kepler (1604) , and the first Cassini, Jean Dominique
(c. 1661).

8. THE TETRABIBLOS

Among the various other works ascribed to Ptolemy, I must
select for discussion his astrological treatise, in spite of the
fact that many men of science would refuse to consider it. 33
Two astrological books bear his name, the Tetrabiblos (Quad-
ripartituni) and the Carpos (Fructus);^ according to the con-
sensus of scholarly opinion, the first is genuine, the second
apocryphal. These two books have been transmitted together
in Greek and other languages, in manuscript and printed tradi-
tions, but for our purpose, it will suffice to consider the first.

Many scholars have claimed that the same man could not
possibly be the author of the rational Almagest and of the
Tetrabiblos, which is chockful of irrational assumptions. They
forget that astrology was the scientific religion of Ptolemy's day.
At a time when the old mythology had become untenable, the
sidereal religion had gradually taken its place in the minds of
men who were loyal to pagan traditions as well as scientifically
minded. Stemming from Greek astronomy and Chaldean
astrology, it was a compromise between the popular religion
and monotheism; the concept of sidereal immortality which
it fostered reconciled astronomy with religion; it was a kind

33 1 have claimed repeatedly that if we would understand ancient
science and culture we must take the errors and superstitions into account
as well as the progressive achievements. See, e.g., my History of Science
(1952), p. xiii.

34 Fructus is the translation of Carpos, but the Latin title more com-
monly used is Centiloquium, referring to the fact that that booklet is a
collection of a hundred aphorisms. The author was probably a court
astrologer who flourished after Ptolemy and before Proclos (V-2) .

59

ANCIENT SCIENCE AND MODERN CIVILIZATION

of scientific pantheism indorsed by men of science as well as
by philosophers, especially by neo-Platonists and Stoics.

We now realize that such a compromise, however useful
it may have been in a period of confusion and distress, was
very dangerous; there was a fatal ambiguity in the astrological
creed, in that it claimed to be science and religion at the same
time. It was a poor application of good science, and the
religious side of it had the weakness of any superstition. There
has never been a better example of pseudo-science and pseudo-
religion. Yet, it prospered for a few centuries in the religious
vacuum caused by the repudiation of the old mythology. It
would be very unfair to blame Ptolemy for having failed to
understand eighteen hundred years ago what many of our own
contemporaries have not yet understood today. The ambi-
guities obtaining between rational knowledge and creed are
still cultivated by pragmatists, by Christian scientists, and other
sectarians who handle religion and science in the way thimble-
riggers cause balls or peas to vanish or reappear.

The Tetrabiblos is dedicated to the same Syros whom
Ptolemy called upon thrice in the Almagest. What is more
convincing, its style is similar to that of the Almagest. It is a
great pity, however, that Ptolemy wrote it, because the prestige
of his name was fully exploited, and the fame of the Tetra-
biblos was not only equal to that of the Almagest, but much
greater.

In his excellent book on Hellenistic Civilization** Pro-
fessor Tarn has developed the view that the triumph of
astrology was assured when Hipparchos and Ptolemy rejected

38 First published in 1927; I quote from the third edition revised by
W. W. Tarn and G. T. Griffith (pp. 298, 348, London, Arnold, 1952).

60

PTOLEMY AND HIS TIME

the heliocentric system of Aristarchos. That theory does not
hold water. In the first place, the postulates of astrology are
independent of whether the Sun or the Earth is the center of
our planetary system; in the second place, astrology did not
stop after the acceptance of the Copernican system but con-
tinued to grow lustily. Kepler himself drew horoscopes. Our
country is leading the world in astronomy, and we have every
right to be proud of that, but if we be honest, we cannot accept
praise for our astronomers without accepting full blame for
our astrologers. There are more astrologers than astronomers
in America and some of them, at least, earn considerably more
than the latter; the astrological publications are far more
popular than the astronomical; almost every newspaper has
an astrological column which has to be paid for and would not
be published at all if a large number of people did not want it.

Astrology was perhaps excusable in the social and spiritual
disarray of Hellenistic and Roman days; it is unforgivable
today. The professional astrologers of our time are fools or
crooks or both, and they ought to be restrained, but who will
do it? Astronomers are too busy with their own work and find
it unnecessary to castigate obvious errors; they do not want to
get into trouble, for in a trial ignorant judges or jurymen
might decide that astrologers have as much right to express
their views as the astronomers. And yet to ignore a contagious
disease is the worst way of dealing with it. If one wishes to cure
it, one must first throw light upon it and show it for what it is.

Superstitions are like diseases, highly contagious diseases.
We should be indulgent to Ptolemy, who had innocently ac-
cepted the prejudices endemic in his age and could not foresee
their evil consequences, but the modern diffusion of astro-
logical superstitions deserves no mercy, and the newspaper

61

ANCIENT SCIENCE AND MODERN CIVILIZATION

owners who do not hesitate to spread lies for the sake of money
should be punished just as one punishes the purveyors of
adulterated food.

To return to the Tetrabiblos Ptolemy refers to the Alma-
gest in his general introduction and explains that the Almagest
is a mathematical book dealing with matters which can be
demonstrated, while the new book deals with matters which
are less tangible and highly conjectural, yet deserve to be in-
vestigated. One has the impression that in his old age, when
Ptolemy had completed his scientific work, he applied himself
to mcia-asironomy and tried to justify as well as he could the
astrological prejudices of his time, prejudices which he fully
shared. The first chapters constitute an apology for divination
and particularly for astrology. Granted the almost universal
beliel in divination, divination by the stars and planets seemed
less irrational, "more scientific," than divination by means of
birds, entrails, dreams or other omina. Ptolemy added that the
possibility and occurrence of error should not discourage the
astrologer any more than they discourage the pilot or the
physician (I, 2) .

The Tetrabiblos is a compilation of Chaldean, Egyptian
and Greek folklore and of earlier writings, especially those of
Poscidonios, 37 which is so complete and so well-ordered that it

36 The original title seems to have been Mathematike tetrabiblos
syntaxis, which was strangely enough the same title as that of the Almagest,
plus the neutral word tetrabiblos. That title was erroneous and mis-
leading, for the Tetrabiblos is definitely not a mathematical treatise.
Some MSS are entitled Ta pros Syron apotelesmatika (Prognostics de-
dicated to Syros). Prognostics was a correct title and meaningful. The
most common title, however, is Tetrabiblos, which means "four books,"
and is as cryptic as Centilo^uium.

87 Poseidonios is not named in the Tetrabiblos, but Franz Boll has
shown, in his Studien iiber Claudius Ptolemdus (Leipzig, 1894) that the

62

PTOLEMY AND HIS TIME

remained a standard work until our own days. In that it was
even more successful than the Almagest, for the simple reason
that astronomy being a science was bound to develop and
change, while modern astrology is essentially the same as the
ancient one. Superstitions may change but do not progress;
in fact, they do not change much, because they are exceedingly
conservative. The Almagest is published anew from time to
time for scholarly purposes, but has no practical value; on
the other hand, new editions of the Tetrabiblos are issued for
the guidance of practising astrologers. 38

The contents of the four books of the Tetrabiblos may be
roughly described as follows: I. Generalities concerning astrol-
ogy and the planets. Beneficent and maleficent planets, mas-
culine and feminine ones, diurnal and nocturnal, etc. II. Catho-
lic astrology, astrological geography and ethnography. Prog-
nostications of a general kind, applying to races, countries,
cities or to catastrophies which affect many men at the same
time, such as wars, famines, plagues, earthquakes, floods, or
the weather, seasons and climes (latitudes). III. Genethlia-
logical prognostications relative to individuals. IV. Fortune.
Astrological aspects of material fortune, personal dignity (axi-
oma), degree of activity, marriage, children, friends and ene-
mies, foreign travel, quality of death, various periods of life.
In Robbins' Greek-English edition (Loeb Library) , the four

author of Tetrabiblos used the lost writings of Poseidonios, especially for
what concerns the defense of astrology and astrological ethnography
(Book II) . In many geographical details, Tetrabiblos and the Geography
do not agree, but it does not follow that the authors of those two works
are different.

88 An English edition published for the astrological market in Chicago,
1936, was reviewed in Isis (35, 181).

63

ANCIENT SCIENCE AND MODERN CIVILIZATION

books cover, respectively, 116, 104, 152 and 87 pages; and the
whole Greek text extends to 230 pages.

One cannot read the whole of that treatise or a part of it
without being terribly dismayed. If Ptolemy was really the
author of it, it is a thousand pities, but that only shows that
he was a man of his clime and time. Even the greatest genius
cannot transcend all those limitations at once.

9. THE PTOLEMAIC TRADITION

We shall outline only the tradition of his three most famous
works, the Almagest, the Cosmography, and the Tetrabiblos.

TRADITION OF THE ALMAGEST

The Greek tradition was solidly established from the be-
ginning and it was kept alive by the commentaries of a series
of illustrious mathematicians, Pappos (1II-2), Theon of Alex-
andria (IV-2), Hypatia (V-l) and Proclos (V-2) . The book
entitled Mathcmatike syntaxis was often called Megale syntaxis
(the great collection) or even Megiste synlaxis (the very great
collection).

The importance of the Arabic tradition is symbolized by the
common name Almagest which combines the Arabic article
with the Greek adjective megiste. Arabic mathematicians were
acquainted with the book very early, for it was translated into
Arabic by an unknown scholar at the insistence of the illus-
trious wazir, Yahya ibn Khalid ibn Barmak (Joannes the Bar-
mecide), who lived from 738 to 805; it was translated again
in 829, on the basis of a Syriac version, by al-Hajjaj ibn Yusuf
(IX- 1) and a third time by Ishaq ibn Hunain (IX-2), and
Ishaq's translation was corrected by Thabit ibn Qurra (IX-2).
Further editions and adaptations were prepared by such

64

PTOLEMY AND HIS TIME

eminent men as Abu-1-Wafa' (X-2) and Nair al-din al-Tusi
(XIII-2).

Meanwhile, the Arabic geographers had produced astro-
nomical treatises which were not translations of the Almagest,
yet were profoundly indebted to it. The first of these treatises
was the one by al-Farghani (IX-1) which became in the ori-
ginal Arabic and in Latin and Hebrew versions one of the
main sources of Ptolemaic astronomy until the Renaissance.
The same can be said of al-Battam's treatise (IX-2) , but though
it was far superior to al-Fargham's, it was less popular. More-
over, since al-Battani was a greater mathematician and a more
original mind than al-Farghani, he modified the Ptolemaic
tradition more deeply.

Not only was it possible to read the Almagest in Arabic, and
the treatises of al-Farghani and al-Battani which were derived
from it, but the Muslim astronomers worked so well that they
were soon able to criticize Ptolemy's ideas. As the astronomical
observations were more numerous and more precise, it became
increasingly difficult to reconcile them with the theories. The
philosopher, Ibn Bajja (Avempace, XII-1), expressed the
difficulties and this was soon done with more authority by Jabir
ibn Aflah (XII-1) in his treatise called Isldh al-magisti, (the
Correction of the Almagest). Other Muslims, the philosopher
Ibn Tufail (XII-2) and his disciple al-BitrujI (XII-2) thought
of solving the difficulties by rejecting Ptolemy's eccentrics and
epicycles and reverting to the earlier theory of homocentric
spheres which had been endorsed by Aristotle himself. After
the twelfth century, the vicissitudes of astronomical theory
were largely the result of a protracted struggle between the
followers of Ptolemy and those of Aristotle. 39

39 For more details, see Intro. 2, 16-19; 3, 110-37, 1105-21.

65

ANCIENT SCIENCE AND MODERN CIVILIZATION

Within the twelfth century, the Almagest as well as the
treatises of Alfraganus and Albategnius 40 became all of them
available in Latin. Alfraganus was first translated by John of
Seville (XII-1) in 1134, then again by Plato of Tivoli (XII-1).

The Almagest was translated from Greek into Latin, in
Sicily, c. 1160, and from Arabic into Latin by Gerard of
Cremona (XII-2) in Toledo in 1175. Such was the prestige of
the Arabic source or of the Toledo academy that the indirect
translation of 1175 displaced the direct one of 1160.

Gerald did not simply translate the Almagest, but he trans-
lated the Isjah al-majisti as well, before 1187 41 (that is, when
Jabir's work was still a novelty in Muslim circles) .

The Hebrew translations were a little slower in appearing;
they belong to the thirteenth century. The summary of the
Almagest written by Ibn Rushd (Averroes, XII-2), the Arabic
text of which is lost, was translated into Hebrew by Jacob
Anatoli (XIII- 1), and the same translated also, c. 1232, al-
Fargham's treatise from Latin and Arabic into Hebrew. Moses
ibn Tibbon (XI1I-2) translated into Hebrew al-Bitruji in 1259
and Jabir ibn Aflah in 1274.

Finally, we may mention, for the sake of curiosty, the
Syriac summary of the Almagest written by Abu-1-Faraj in 1279;
this was probably the redaction of his lectures on the subject
delivered at Maragha between 1272 and 1279.

In short, during the medieval period, every astronomer,
whether Jewish, Christian or Muslim, might be assumed to be
familiar with Ptolemaic astronomy, directly or indirectly; we
might even say that every one was a Ptolemaist with few, if

40 Meaning al-Fargham (IX-1) and al-Battani (IX-2).

41 1187 is the year of Gerard's death in Toledo. Jabir (Latin, Geber)
died about the middle of the twelfth century.

66

PTOLEMY AND HIS TIME

any, qualifications. The history of medieval astronomy is a
history of Ptolemaic ideas and of a growing discontent with
them. The difficulties could not be solved with cinematical
expedients, nor could they be solved by replacing the Sun in
the center instead of the Earth. The main stumbling block
was the notion that celestial trajectories must be circular (or
combinations of circles) and that block was removed only by
Kepler as late as 1609.

The history of the Ptolemaic tradition includes the history
of astronomical tables, all of which were ultimately derived
from those of the Almagest.

One more aspect of the Ptolemaic tradition must be in-
dicated, however. The Almagest consecrated the use of sexa-
gesimal fractions, and obstructed the natural extension of
decimal numbers to decimal fractions; or to put it otherwise,
it discouraged the use of decimal submultiples in the same
manner that decimal multiples were used. The superiority of
decimal fractions was well explained for the first time by the
Fleming Simon Stevin in 1585, and their exclusive use has not
been obtained to this day.

With the slowness of progress, or the persistance of Ptole-
maic errors, the geocentric error was not proved until 1543 by
Copernicus, the sexagesimal error not until 1585 by Stevin,
the circular error not until 1609 by Kepler.

The first printed edition of Ptolemaic astronomy was al-
Fargham's treatise as Latinized by John of Seville (XII-1),
Compilatio astronomica (Ferrara, 1493. Klebs no. 51. Facsimiles
of both sides of first leaf, Osiris 5, 141) .

The Epitoma in Almagestum by Regiomontanus (XV-2)
was printed three years later (Venice, 1496. Klebs no. 841.1.
Facsimile of title page, Osiris 5, 162) .

So much for the incunabula.

67

ANCIENT SCIENCE AND MODERN CIVILIZATION

The first printed editions of the Almagest are the following:
Latin version from the Arabic by Gerard of Cremona, Toledo,
1175, edited by Peter Liechtenstein (Venice, 1515).

Latin version from the Greek by George of Trebizond,
1451, edited by Luca Gaurico (Venice, Junta, 1528) .

First Greek text, edited by Simon Grynaeus, made upon
the Bessarion manuscript once used by Regiomontanus (Basel,
Walderus, 1538). Facsimile of title page (I sis 36, 256).

The following indications may be of interest.

First printed edition of al-Battam (IX-2), in the Latin
translation by Plato of Tivoli (XII- 1) (Nurnberg, Joh. Pet-
reius, 1537). Splendid Arabic-Latin edition by C. A. Nallino
(3 vols., Milano, 1899-1907).

First printed editions of the Isldh al-majistl of Jabir ibn
Aflah (XII-1) as Latinized by Gerard of Cremona before 1187
(Nurnberg, Joh. Petreius, 1534).

First printed edition of al-Bitruji (XII-2), as Latinized
by Qalonymous ben David in 1528-29 (Venice, Junta, 1531).
The tradition of this text is curious. It was translated from
Arabic into Latin by Michael Scot in 1217, 42 from Arabic into
Hebrew by Moses ibn Tibbon in 1259, from Hebrew into
Latin by Qalonymos.

To these printed texts a good many others could be added,
even if one restrict oneself to the pre-Copernican period (pre-
1543). It will suffice to mention the many editions of the
Sphaera mundi by Joannes de Sacrobosco (XIII- 1) , which was
slavishly derived from al-Farghani and al-Battani. There are
thirty-one separate incunabular editions of the Sphaera, plus
many others in combination with other texts. 43

48 Michael Scot's translation was recently edited by Francis J. Carmody
(Berkeley, Calif., 1952; Isis 44, 280-81) .

48 For Sacrobosco, see Klebs (nos. 874, 875). Lynn Thorndike, The
Sphere and its Commentators (Chicago, 1949; Isis 40, 257-63).

68

PTOLEMY AND HIS TIME

TRADITIONS OF THE GEOGRAPHY (OR COSMOGRAPHY)

The early tradition of the Cosmography is not by any
means as well known as that of the Almagest. We have already
explained that in this case it does not suffice to consider the
text, but there is also a cartographic tradition which is very
mysterious.

The Cosmography was known in Syriac circles; witness
a chapter of the Syriac Chronicle of 569, and the Hexaemeron
of Jacob of Edessa (VII-2) . Much was added to it by Muslim
geographers, such as al-Khwarizmi (IX- 1), al-Battam (IX-2),
and many others, East and West.

The Latin translation of the Greek text was made by
Giacomo d'Angelo (Jacobus Angelus) in 1409.

The growing popularity of the Cosmography in the fifteenth
century is well illustrated by the number of incunabula. While
there was no incunabula edition of the Almagest (excepting
Regiomontanus' Epitoma of 1496), there were seven of the
Cosmographia (Klebs no. 812). The first was issued by Her-
mann Liechtenstein (Vicenza, 1475); the first with maps by
Lapis (Bologna, 1477) ; 44 facsimile copy of the edition of 1477
(Klebs no. 812.2) by Edward Lynam: The First Engraved
Atlas of the World (26 maps, Jenkintown, George H. Beans,
1941).

The first Greek edition was prepared by no less a person
than Erasmus (Basel, Froben and Episcopius, 1533) .

44 Not 1462 as printed by mistake in its colophon (Osiris 5, 103). First
and last page of the first edition, 1475 (Osiris 5, 134-35) .

69

ANCIENT SCIENCE AND MODERN CIVILIZATION

TRADITION OF THE TETRABIBLOS

The Tetrabiblos must have been a popular book in Greek
circles, because astrological fancies and other aberrations
flourished more and more as the old culture was decaying, but
the ancient tradition is obscure. An introduction to it is
ascribed to Porphyries (III-2), a paraphrase to Proclos (V-2),
and there is an anonymous commentary which might also be
by the latter. That is not much to go by. 45

TheTetrabiblos was one of the earliest Greek books to be
translated into Arabic, under al-Mansur (VIII-2), the second
'Abbasi caliph (754-75), the founder of Baghdad the trans-
lator being Abu Yahya al-Batriq (VIII-2). Al-Batriq's version
was commented upon by 'Umar ibn al-Farrukhan (IX- 1), and
by Ahmad ibn Yusuf (1X-2). The Tetrabiblos was translated
again by Hunain ibn Ishaq (IX-2) and this translation was
commented upon by 'All ibn Ridwan (XI- 1); 'All's commen-
tary was much used by astrologers.

Another translation by Ibrahim ibn al-Salt (date un-
known) corrected by Thabit ibn Qurra (IX-2) and (or) Hun-
ain ibn Ishaq was Latinized by Plato of Tivoli (XII- 1) and
was the first Ptolemaic work to be translated into Latin. A
new Latin translation was made in 1206 by an unknown
scholar. The Tetrabiblos and 'All ibn Ridwan's commentary
upon it were translated into Spanish, perhaps by Judah ben
Moses (XIII-2), for Alfonso el Sabio (XIII-2) , and from
Spanish into Latin by Aegidius of Thebaldis soon after 1256.

45

The Greek text of the paraphrase was published with a preface by
Philip Melanchthon (Basel, J. Oporinus, 1554), a Greek-Latin edition of
the two other texts by Hieronymus Wolf was published a few years later
(Basel, Petreius, 1559).

70

PTOLEMY AND HIS TIME

Still another Latin translation was prepared, c. 1305, by Simon
de Bredon (XIV-1) . Etc.

The Latin version from the Arabic was printed very early.
There are two separate incunabula, the first by Ratdolt (Ven-
ice, 1484) and the second by Locatellus (Venice, 1493), plus
many included in other incunabula editions (Klebs no. 814).

There were also Latin versions from the Greek, one being
mentioned by Henry Bate of Malines (XIII-2) in 1281. The
first edition of the Greek text, by Joachim Camerarius was
printed by J. Petreius of Nurnberg in 1535, and reprinted by
Joannes Oporinus at Basel in 1553. Both editions included
Latin translations from the Greek, the first by Camerarius and
the second by Philip Melanchthon; both included also the
Carpos in Greek and Latin.

An English translation by the Dublin quack, John Whalley,
was printed in London in 1701 and again in 1786. Another
English translation by J. M. Ashmand in London in 1822 was
reprinted there in 1917 and in Chicago in 1936 (his 35, 181).

Two critical editions of the Greek text were published in-
dependently in 1940, the one by Franz Boll and Aemilia Boer
in the Opera omnia of Ptolemy (III, 1, Teubner, Leipzig)
and the other by Frank Egleston Robbins, with an English
version, in the Loeb Classical Library (reprinted in 1948;
7^33,718-19).

There are thus three English versions of the Tetrabiblos.
Until 1952, this was the only Ptolemaic text which could be
read in our language. Horresco referens! (Isis 44, 278).

71

ANCIENT SCIENCE AND MODERN CIVILIZATION

10. BIBLIOGRAPHY OF PTOLEMY

1 . Complete Works

Opera quae extant omnia. Edited by J. L. Heiberg (Teub-
ner, Leipzig, 1898 f.). Vol. I in 2 vols., Almagest (1903). Vol. II,
Opera astronomica minora (1907). Vol. Ill, 1, Tetrabiblos
edited by Franz Boll and Aemilia Boer (1940).

This is all in Greek, except when the Greek text is lost.

2. The Almagest

The standard edition is Heiberg's in the Opera omnia (Vol.
I in 2 vols, 1898-1903). The Greek-French edition by the Abbe"
Nicolas B. Halma with notes by J. B. J. Delambre is very con-
venient (2 vols., Paris, 1813-16). Facsimile reprint of smaller
size (Paris, Hermann, 1927) .

German translation by Karl Manitius derived from the
Heiberg text (2 vols., Leipzig, 1912-13).

An English translation by Catasby Taliaferro is included in
Great Books of the Western World (XVI, 1-478, Chicago,
1952; 7sw 44, 278-80).

Christian H. F. Peters and Edward Ball Knobel. Ptolemy's
Catalogue of Stars. A revision of the Almagest (208 pp.,
Carnegie Institution of Washington, 1915; Isis 2, 401) .

3. The Geography

Ptolemaei Geographiae Codex Urbinas Graecus 82. Edited
by Joseph Fischer and Pius Francus de Cavalieri (4 vols.,
Leiden, Brill, 1932). For fuller description and review, see
Isis 20, 266-70). This includes an elaborate study of Ptolemy
and his Geography by Father Fischer with indices (Tomus
prodromus, pars prior, 624 pp.).

Traite de geographic traduit pour la premiere fois du grec
en francais sur les MSS de la Bibliotheque du Roi par l'abb
Halma (quarto 214 pp., Paris, 1828) , not seen.

Geography of Ptolemy, translated into English by Edward
Luther Stevenson (folio, 183 pp., 29 pi., New York Public

72

PTOLEMY AND HIS TIME

Library, 1932; his 20, 270-74; 22, 533-39) . No index. Imperfect
translation.

Let us hope that the edition of the Greek text being pre-
pared for the Opera Omnia will soon appear. Thus far, we
have no better edition of the Greek text than that of Carolus
Miiller: Ptolemaei Geographia (2 vols., Paris, Firmin Didot,
1883-1901), with Latin translation; but it is incomplete (stop-
ping at vol. V, cap. 19), and hence lacks an index.

For an index, one must refer to the old Greek edition of

C. F. A. Nobbe (Ed. stereotype, 3 vols., Leipzig, Tauchnitz,

1843-45) , or the old Nomenclator which the Fleming Abraham

Ortelius (1527-98) added to his Theatrum orbis terrarum

(Antwerp, 1579) and later editions and also published separate-

'y-

Two bibliographies may be added. Henry Newton Stevens:
Ptolemy's Geography. A Brief Account of all the Printed Edi-
tions down to 1730 (62 pp., London, Stevens and Stiles, 1908).
William Harris Stahl: Ptolemy's Geography (86 pp., New York
Public Library) . This is especially useful to find studies de-
voted to the Ptolemaic account of specific regions, say, Sicily
or Ceylon.

4. Alia

For editions of the Optics or Tetrabiblos, see chapters 7-8
above devoted to these books. For additional bibliography,
see my Introduction (1 , 274-78) and the Critical Bibliographies
of Isis, section II- 1.

73

THE END OF GREEK SCIENCE AND CULTURE

(from c. 300 to 529)

LE,

CAVING out of the question prehistoric times,
which cannot be measured, Greek culture begins with Homer
(say, in the ninth or eighth centuries); Greek science begins a
little later with Thales and Pythagoras (sixth century). My
first lecture on Euclid (c. 300 B.C.) dealt with a relatively late
stage of Greek culture, the so-called Hellenistic. In order to
deal with Ptolemy in my second lecture, we had to make a
jump of more than four centuries; we shall now consider a
period which begins 150 years and ends 350 years later. This
illustrates once more the length of ancient Greek culture, its
duration and its inexhaustible variety. The Roman world of
Ptolemy was very different from the Alexandrian of Euclid

75

ANCIENT SCIENCE AND MODERN CIVILIZATION

and the world which I shall try to evoke here is again extremely
different.

The Roman Empire and Christianity were born at about
the same time. By the beginning of the fourth century the
Roman Empire was going down rapidly while Christianity
was going up, and we witness the symbiosis of the old Pagan
moving slowly to his death and of the Christian youth prepar-
ing to live and conquer.

This lecture will be divided into three parts: Greek mathe-
tics, Greek medicine, and the philosophical and religious back-
ground. My reason for speaking of the background in the last
part instead of the first will be apparent later on.

1. GREEK. MATHEMATICIANS

Ptolemy's gigantic efforts were followed by a lull of more
than a century. So much so that when the next great
mathematician appeared he felt obliged to prepare a sum-
mary of earlier books, under the title Mathematical Collection
(synagoge). This mathematician was Pappos of Alexandria.
According to a scholion (marginal note) in an old manuscript,
he lived under Diocletian (emperor, 284-305) and therefore it
is tempting to consider him a man of the third century like
the algebraist Diophantos, 1 but according to Canon Rome 2
Pappos' commentary on the Almagest was probably written
after 320 and the Mathematical Collection even later. Pappos
wrote various commentaries on Euclid and Ptolemy, but his

1 That was done in my Introduction, where Pappos was placed in the
time of Diophantos (III-2) . It would have been better, perhaps, to place
him in (IV-1) (Intro. 3, ix) . Pappos would seem to be half-way between
Diophantos and Theon of Alexandria.

a Adolphe Rome: "Sur la date de Pappus" (Annales de la Soctttt
scientifique de Bruxelles, serie A [1927], 46-48), Isis 11, 415-16.

76

THE END OF GREEK SCIENCE AND CULTURE

main work is the Synagoge already mentioned, of which a
great part has come down to us. It is divided into eight books;
we have everything except Book I and chapters 1 to 13 of
Book II, the preface to IV, and perhaps the end of VIII. It is
difficult to analyze it because it is devoted to a multiplicity of
mathematical subjects and combines for most of them old and
new. Pappos was not a teacher like Euclid or Ptolemy but a
learned man who was familiar with the whole of Greek mathe-
matics and tried to summarize it in his own peculiar way. He
was a good commentator because he was on a level with his
greatest predecessors and was able to add ingenious theorems
and problems of his own, but he was not very methodical. As
far as we understand the general composition of his Synapoge,
he had taken notes on the mathematical classics, invented and
solved new problems, and then classified them in eight books.
Each book is preceded by general reflections which give to that
group of problems its philosophical, mathematical and his-
torical setting. These prefaces are of deep interest to historians
of mathematics and, therefore, it is a great pity that three of
them are lost (the prefaces to Books I, II and IV) . They may
turn up some day in an Arabic version.

The following notes will indicate roughly the contents of
the Synagoge, book by book.

Book II (chapters 14-16). Commentary on Apollonios*
method for the writing of large numbers in terms of powers of
myriads (10,000 n ) and for operating with them.

Book III. History of the problem: to find two mean pro-
portionals in continued proportion between two given straight
lines. Classification of geometrical problems in three classes
(1) plane, (2) solid, (3) those requiring the use of higher
curves for their solution. Curious propositions suggested by

77

ANCIENT SCIENCE AND MODERN CIVILIZATION

the paradoxes of Erycirios (otherwise unknown). How to ir
scribe the five regular solids in a given sphere.

Book IV. Extension of the Pythagorean problem on th
square of the hypotenuse. Circles inscribed in the arbelc
(semicircular knife used by cobblers) , commentary on a boo
of Archimedes (lost in Greek, preserved in Arabic) . Discussio:
of Archimedes' spiral, Nicomedes' conchoid, the quadratri>
spherical spiral. Trisection of any angle, etc. This include
a method of integration (for the spiral) different from that c
Archimedes.

Book V. Isoperimetry, derived from Zenodoros (II- 1 B.C/
The delightful preface refers to the bees whose cells are bui]
with a great regularity and a marvelous economy of space
Pappos did not deal only with plane problems; he also state*
that the sphere has the greatest volume for a -given surface.

Book VI, mainly astronomical, being inspired by some c
the authors of the "little astronomy," Autolycos (IV-2 B.C.
Aristarchos (III-l B.C.), Euclid (III-l B.C.), Theodosios (I-
B.C.) and Menelaos (1-2) . 3

Book VII is by far the longest book of the collection; th
longest books next to it are III, IV and V, but VII is almos
as long as these three books put together. It is also the mos
important for historians, because it discusses a good many los
books of Aristaios (IV-2 B.C.), Euclid, Apollonios, an

3 The "little astronomy" or ho micros astronomumenos (topos) w;
so called perhaps by contrast with the megale syntaxis. Many of the*
writings were transmitted together (in the same manuscripts) to Grec
readers and later to Arabic ones. The Arabic collection, including th
Greek texts plus some original Arabic ones, was called Kitdb al-mutt
ivassitdt bain al-handasa wal-hai'a, The middle books between geometi
and astronomy (Intro. 2, 1001) .

78

THE END OF GREEK SCIENCE AND CULTURE

1. THE ARBfiLOS

A C B

2. INSCRIPTION OF THREE CIRCLES IN THE ARBELOS

If P, Q, R are the centers of these circles, d lt d 2 , d a their diameters, P lf P 2 ,
p 8 the distances of the centers to the base line, then p a = d^a = 2d 2 p a =
3d 8 p 4 = etc.

From Heath: Manual of Greek Mathematics, Oxford, 1931, p. 442; I sis
16, 450.

79

ANCIENT SCIENCE AND MODERN CIVILIZATION

Eratosthenes. 4 According to its own title, it contains the
lemmata of the "solved locus" (ho topos analyomenos), and is
a kind of textbook on geometrical method for advanced stu-
dents. It was dedicated (as well as Book VIII) to Pappos' son
Hermodoros. After a preface wherein he defines and explains
analysis and synthesis, he deals with each of those ancient
treatises, stressing one point or another. For example, we find
in it the famous Pappos' problem: "given several straight lines
in a plane, to find the locus of a point, such that when straight
lines are drawn from it to the given lines at a given angle,
the products of certain of the segments shall be in a given
ratio to the product of the remaining ones." This problem is
important in itself, but even more so because it exercized
Descartes' mind and caused him to invent the method of co-
ordinates explained in his Geometric (1637). Think of a seed
lying asleep for more than thirteen centuries and then helping
to produce that magnificent flowering, analytical geometry.
Another proposition was the seed of the centrobaric method;
it proves a theorem equivalent to the Guldin theorem: "if a
plane closed curve rotates around an axis, the volume created
by its revolution will be equal to the product of the area by
the length of the path of its center of gravity." The Jesuit
father Paul Guldin published that theorem more clearly in
1640. 8

4 No less than twelve treatises in 33 books, most of them by Euclid
(3 treatises in 6 books) and Apollonios (7 treatises in 20 books).

6 The Guldin anticipation in Pappos is imperfect and perhaps an inter-
polation; it does not occur in all the manuscripts. Guldin expressed the
theorem very clearly for the first time but his proof is incomplete. The
first complete proof was given by his adversary, Bonaventura Cavalieri, in
1647.

80

THE END OF GREEK SCIENCE AND CULTURE

Another problem bearing Pappos' name is not in his Col-
lection, however. Given a point A on the bisectrix of a given
angle, to draw through A, a segment a ending on both sides of
the angle. This problem had an extraordinary fortune, prob-
ably because of this singularity: it leads to an equation of the
4th degree and yet can be solved with ruler and compass. 6

The most astonishing part of that Book VII has not yet
been mentioned. Dealing with the lost treatise of Apollonios
on the determinate section (diorismene tome), Pappos ex-
plains the involution of points.

The final Book VIII is mechanical and is largely derived
from Heron of Alexandria. Following Heron, Pappos dis-
tinguished various parts of theoretical mechanics (geometry,
arithmetic, astronomy and physics) and a practical or manual
part. This book may be considered the climax of Greek me-
chanics and helps us to realize the great variety of problems
to which the Hellenistic mechanicians 7 addressed themselves.
Many needs had to be filled: the moving of heavy bodies, war
engines for offensive or defensive purposes, machines for the
pumping of water, automata and other gadgets for the use of
wonder workers; water clocks and moving spheres. Pappos was
interested in practical problems, such as the construction of
toothed gearings and of a cylindrical helix (cochlias) acting
upon the teeth of a wheel, but he was even more concerned
with mathematical methods, such as the finding of two mean
proportionals between two given lines, the determination of

A thick volume was devoted to it by A. Maroger: Le Probleme de
Pappus et Ses Cent Premieres Solutions (Paris, Vuibert, 1925) , reviewed
in Revue Generate des Sciences (37, 338) .

7 Pappos knew them chiefly through Heron; Philon is quoted only a
few times, Ctesibios not at all.

81

ANCIENT SCIENCE AND MODERN CIVILIZATION

centers of gravity, the drawing of a conic through five given
points. The mathematician in him was so keen that he was
trying to solve theoretical problems such as this one: how to
fill the area of a circle with seven equal regular hexagons.

If Book VIII is the climax of Greek mechanics, we may say
as well that the whole Collection is a treasury and to some
extent the culmination ol Greek mathematics. Little was
added to it in the Byzantine age and the Western world, hav-
ing lost its knowledge of Greek together with its interest in
higher mathematics, was not able to avail itself of the riches
which Pappos had put together. The ideas collected or in-
vented by Pappos did not stimulate Western mathematicians
until very late, but when they finally did, they caused the
birth of modern mathematics analytical geometry, projective
geometry, centrobaric method. That birth or rebirth, from
Pappos' ashes, occurred within four years (1637-40). Thus was
modern geometry connected immediately with the ancient one
as if nothing had happened between.

Pappos was the greatest mathematician of the final period
of ancient science, and no one emulated him in Byzantine
times. He was the last mathematical giant of antiquity. Never-
theless, he was followed by a very distinguished group of
mathematicians, so numerous indeed that it will not be pos-
sible to speak of each of them except in the briefest mannef.
Serenos of Antinoopolis (IV-1) was another Egyptian Greek,
hailing from the city in Middle Egypt which Hadrian had
founded in memory of the beautiful Antinoos, drowned in the
Nile in 122. We must assume that Serenos studied or flourished
in Alexandria, and in any case he was in touch with the Alex-
andrian school, the greatest mathematical school of his age as
well as the one which was nearest to him. He wrote a com-

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THE END OF GREEK SCIENCE AND CULTURE

mentary on the Conies of Apollonios and two original treatises
on the sections of cylinders and cones.

And now let us consider two other illustrious Alexandrians,
father and daughter, Theon (IV-2) and Hypatia (V-l), both
teachers in the Museum. Theon edited Euclid's Elements and
wrote a very elaborate commentary on the Almagest. He com-
pleted Ptolemy's establishment of sexagesimal fractions; Hy-
patia revised her father's commentary on Books III and follow-
ing of the Almagest and she may be responsible for a new
method of sexagesimal division closer to the Babylonian than
her father's, but it is impossible to know exactly what belongs
to either of them. Her own commentaries on Apollonios,
Ptolemy's Canon (chronology) and Diophantos are all lost,
but she is immortalized by the grateful letters of Synesios of
Gyrene (V-l) 8 and, above all, by her martyrdom in 415. She
enjoys the double honor of being the first female mathe-
matician and one of the first martyrs of science.

After Hypatia's death, there was a lull in the mathematical
(pagan) school of Alexandria, and no wonder. The next
leaders belong to the following century, Ammonios and Philo-
ponos. Ammonios, son of Hermias (VI-1), studied under
Proclos in Athens, but he restored the school of Alexandria
and, judging by the merit of some of his pupils, must have

8 Synesios of Gyrene (c. 370 c. 11'}) was converted in middle age (c.
407) and became soon afterward bishop of Ptolemais (410), one of the
five cities of Cyrenaica (Pentapolis). Of his letters 159 have been pre-
served, dating from 394 to 413; seven are addressed to Hypatia covering the
same lapse of time. In letter 15, he asked her to have a baryllion (a kind
of hydrometer) made for him. This is the first description of that instru-
ment in literature, but its use is such an obvious application of Archime-
dian hydrostatics that some Hellenistic mechanician had probably ii/vcntcd
it long before the fifth century.

83

ANCIENT SCIENCE AND MODERN CIVILIZATION

been a great teacher. He divided mathematics into four
branches: arithmetic, geometry, astronomy, music a division
which became in the Latin world the quadrivium. 9 His dis-
ciple, Joannes Philoponos (VI-1), 10 was primarily a philosopher,
but he wrote the earliest treatise on the astrolabe and a com-
mentary on the arithmetic of Nicomachos.

Now, let us return to Athens. When it had become a pro-
vincial city of the Roman empire, its schools were eclipsed by
the Museum, yet it continued to be the sacred metropolis of
Hellenism. Political and commercial power had withdrawn,
but philosophy had remained. Yet, it must be admitted that
by the end of the fourth century, only one of the four main
schools was really alive. We cannot name the headmasters or
leaders of the Aristotelian, Stoic and Epicurean schools. Only
in the Academy was the succession (diadoche) of the head-
masters preserved. Let us name them for the sake of curiosity:
Priscos (c. 370), Plutarchos, son of Nestorios 11 (d. 431), Syrianos
of Alexandria (V-l), Domninos of Larissa (V-2) , Proclos the
Successor (V-2), Marines of Sichem (V-2) , Isidores of Alex-
andria, Hegias, Zenodotos, and finally Damascios (VI-1).

The word quadrivium was introduced by Ammonios' Latin con-
temporary, Boetius (VI-1) , but the idea is considerably older. It was
adumbrated by Archytas of Tarentum (IV- 1 B.C.), for whom see my
History of Science (pp. 434, 440, 521) .

10 Joannes Philoponos is identical with John the Grammarian (Intro. 1,
421, 480) . He was a Jacobite Christian and one of the very greatest per-
sonalities of his age (Isis 18, 447).

11 The decadence of the age is illustrated by the fact that this Plutarchos
was called the Great! Plutarchos of Athens is now almost unknown. When
referring to his illustrious namesake, Plutarchos of Chaironeia (1-2), I
shall call the latter "Plutarch," because he belongs to world literature.
Plutarchos' daughter, AsclSpigeneia, was a "femme savante," the Athenian
contemporary and counterpart of the Alexandrian Hypatia.

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THE END OF GREEK SCIENCE AND CULTURE

This list suggests two remarks. First, it is probably com-
plete 12 and thus proves a modicum of continuity, but the fact
that many of the diadochoi are all but unknown is an ominous
sign. Who were Priscos, Hegias and Zenodotos? As to the last
head of the Academy, we do not even know his personal name,
for Damascios simply means the Damascene. Second, an
analysis of the list would show that the schools of Athens and
Alexandria were relatively close to each other. Ammonios was
a pupil of Proclos and a teacher of Damascios; it is a regular
chasse-croise. Alexandrians would study in Athens and Athen-
ians in Alexandria. Two at least of the diadochoi of the
Academy, Syrianos and Isidores, were Alexandrians.

It is clear that the Academy had ceased to be a high mathe-
matical school. The majority of the teachers and students
were interested only in Neoplatonic arithmetic, that is, number
mysticism. However, Domninos of Larissa tried to react
against that and to revive the Euclidian theory of numbers.
Proclos was by far the greatest headmaster in the last century
of the Academy's existence. He was of Lycian origin 13 but born
at Byzantion; he studied in Alexandria, but too late to drink at
the sources of Hypatia's wisdom; he went back to Athens and
was head of the Academy until his death in 485. He has been
called "the Hegel of Neoplatonism" by people who wanted
to praise him as much as possible; he was certainly more in-
fluential as a philosopher than as an astronomer or a mathe-
matician. Yet we owe him gratitude for his introduction to
Ptolemaic astronomy and his commentary on Book I of the

18 Ten headmasters seem enough to cover a period of 150 years.

18 In our list of the last ten headmasters of the Academy, only seven are
of known origin; six of these came from Egypt or Western Asia; only one
(Plutarchos) was Athenian. Simplicios also came from the Near East.

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ANCIENT SCIENCE AND MODERN CIVILIZATION

Elements. That commentary is of considerable value for the
history of Euclid's sources; much of the information which is
thus conveyed to us was derived from the lost works of two
Rhodians, Eudemos (IV-2 B.C.) and Geminos (1-1 B.C.).
Without Proclos, our knowledge of ancient geometry would be
considerably poorer than it is.

Marinos of Sichem wrote a preface to Euclid's Data (ex-
ercises of geometry), but Damascios did not write the "XVth
book of Euclid" ascribed to him.

The greatest mathematician who flourished at Athens in
the sixth century has not yet been named, for he was not a
headmaster of the Academy, that is, Simplicios (VI-1) . His
Aristotelian commentaries contain many items of mechanical
and astronomical interest and he composed a commentary on
Euclid I. The Cilician Simplicios and the Egyptian Philoponos
were the outstanding men of science of their age.

One last remark about the Academy. From the end of the
third century, it was the only philosophical school left in
Athens, but that was at the price of its own integrity. The
Academy had ceased for centuries to be Platonic; not only was
its prevailing philosophy Neoplatonic but it gave hospitality
to other philosophies and was ready to discuss them all and to
syncretize them. Syrianos, Proclos, Marinos wrote commen-
taries on Aristotle; Simplicios wrote one on Epictetos.

In addition to the mathematical schools of Alexandria and
Athens there was also in the first half of the sixth century a
new school in Constantinople, illustrated by Isidores of Miletos
and his pupil Eutocios of Ascalon, but their main activities
were probably posterior to the closing of the Academy. 14 The

14 And hence outside of the scope of this lecture. The same may be
said of Philoponos and Simplicios.

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THE END OF GREEK SCIENCE AND CULTURE

Constantinopolitan mathematicians were probably Christians,
not so any of the others, except Philoponos, who was a Mono-
physite.

We have spoken of a dozen mathematicians. Instead of
considering the tradition of each of them, we shall restrict our-
selves to five, Pappos, Serenos, Theon, Hypatia and Proclos.

The tradition of Pappos is exceptional in that it involves
Armenian literature, for Moses of Chorene (V-l), who had been
educated in Alexandria, wrote in Armenian a Geography
which was based on Pappos' lost work ad hoc. The commen-
tary on the Almagest was amplified by Theon; his commentary
on the Elements of Euclid was used by Proclos and Eutocios.
The part of it devoted to Book X, lost in Greek, was preserved
in the Arabic version of Abu 'Uthman al-Dimishqi (X-l) .
Abu-1-Wafa' (X-2) derived his knowledge of the solid poly-
hedra from Pappos' Collection.

The first Greek edition of the Almagest (Basel, J. Walderus,
1538) 15 included Pappos' commentary to Book V.

The first printed edition of the Collection was the Latin
translation from the Greek by Federigo Commandino (Pesaro,
Hier. Concordia, 1588), reprinted in Venice, 1589, and Bolog-
na, 1660. The first complete edition of the Greek text appeared
only three centuries later; it was admirably prepared by
Friedrich Hultsch (3 vols., Berlin, 1876-78) , 16

William Thomson: The Commentary of Pappos on Book X
of Euclid's Elements, Arabic text and translation (Cambridge,
Harvard, 1930; Isis 16, 132-36).

16 Facsimile of title page in Isis 36, 256.

16 Hultsch's edition was a model followed by later editors of Greek
mathematical texts such as Heiberg. For Friedrich Hultsch (1833-1906),
see Tannery, Mdmoires 75, 243-317; Isis 25, 57-59) .

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ANCIENT SCIENCE AND MODERN CIVILIZATION

Adolphe Rome: "Pappus, Commentaire sur les livres 5 ct
6 dc 1'Alniageste" (Studi c testi 54, Vatican, 1931; Isis 19, 381),
Greek text.

Paul Ver Eecke: Pappus. La Collection mathematique (2
vols., Bruges, 1933; Isis 26, 495), French translation.

The early tradition of Sercnos was mixed up with the
Apollonian tradition in both Greek and Arabic. The first
printed text was the Latin version which Federigo Com-
rnandino published in his Apollonios (Bologna, Alex. Benatius,
1566). The first Greek edition was included in the splendid
Greek-Latin edition of Apollonios by Edmund Halley (Ox-
ford, 1710). New Greek-Latin edition by J. L. Heiberg (Leip-
zig, 1896). French translation by Paul Ver Eecke (208 pp.,
Bruges, 1929; Isis 15, 397).

Theon's commentary on the Almagest, as revised by his
daughter Hypatia, was known to the Byzantine mathematicians
Nicolaos Cabasilas (XIV-2) and Theodoros Meliteniotes (XIV-
2). It was included in the first Greek edition of the Almagest
(Basel, 1538). A new Greek edition, with French translation,
was begun by Nicolas Halma (Paris, 1813-16). An exemplary
edition of the Greek text was begun by Adolphe Rome in
1936; thus far, it extends to Books I-IV (Vatican, 1936-1943;
Isis 28, 543; 36, 255) ; the continuation is being prepared by
his disciple, Joseph Mogenet.

Proclos ,was far more popular as a philosopher, theologian,
and even as a physicist than as a mathematician, and the tra-
dition of his many writings is very complex. We shall consider
here only his mathematical work. Isaac Argyros (XIV-2) re-
vised his commentary on the arithmetic of Nicomachos. His
commentary on Euclid, Book I, was first printed in Greek in
Simon Gryneus' Greek edition of Euclid (Basel, Hervagius,
1533). Latin editions were prepared by Franciscus Barocius
(Padova, Gratiosus Perchacinus, 1560) and by Federigo Com-
mandino with Euclid (Pesaro, 1572). Critical Greek edition by
Gottfried Friedlein (515 pp., Leipzig, 1873). French transla-
tion by Paul Ver Eecke (396 pp., Bruges, 1948; Isis 40, 256).

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THE END OF GREEK SCIENCE AND CULTURE

The tradition of the final mathematical achievements of
Hellenism is curious in at least two respects. In the first place,
it hardly involved the Arabic detour, except in the case of
Pappos. Their rediscovery was largely due to Byzantine
scholars and later to Renaissance ones, with the result that
Greek printed editions were anterior to the Latin ones, except
in Serenos' case. As far as the Latin tradition is concerned,
the lion's share was done by Federigo Commandino of Urbino
(1509-75), especially if one considers that he was the first to
publish Pappos' Collection, the influence of which upon later
mathematicians was considerable.

2. BYZANTINE MEDICINE

For the sake of simplicity it will be best to deal with only
one physician, the greatest of this age, 17 Oribasios (IV-2), and
we call him Byzantine rather than Greek or Hellenistic be-
cause he was a physician to the Byzantine court in Con-
stantinople. Oribasios was born in Pergamon like his pre-
decessor Galen (II-2), of whose fame he was the main artisan.
His greatest work was a medical encyclopedia, latricai syna-
gogai, of such immense size that only one third of it has come
down to us; the original extended to seventy books. 18 It is of
great value for historians, for it has helped to preserve a good
many earlier medical texts which would have been lost other-
wise; its numerous quotations are always referred to their

1T Aetios of Amida (VI-1), Justinian's archiater, comes just after its
end. For a general view of Byzantine medicine, see Isis 42, 150, or my
Philadelphia lectures (1954).

" We have only Books I to XV, XXI-XXII, XXIV-XXV, XLIV-LI, with
lacunas a total of less than 27 books.

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ANCIENT SCIENCE AND MODERN CIVILIZATION

authors. Oribasios was befriended by Prince Julian, 19 became
his physician, and was almost the only person to whom the
latter revealed his apostasy. In 355, when Julian was made a
Caesar and sent to Gaul, he took Oribasios with him. During
his brief rule (361-63), he appointed him quaestor of Con-
stantinople and charged him to go to Delphoi in order to con-
sult the oracle and possibly revive its glory; that undertaking
ended in failure 20 but Julian did not take it ill and con-
tinued to favor his physician. He encouraged him to write his
medical encyclopedia, and when he started on his last cam-
paign against Persia, Oribasios went with him and was with
him at Antiocheia and at the moment of his death on the
battlefield on 26 June, 363. It is clear that Oribasios shared
the pagan faith of his master. This is sufficiently proved by
the facts already mentioned but also by the persecution which
he suffered after his protector's death. The Christian emperors
who followed Julian the Apostate, Valens and Valentinian,

"Julian, born in Constantinople in 331, was but a few years younger
than Oribasios, born c. 325. While he was wintering in Paris, 358-59,
Julian wrote to Oribasios, then in Vienne, a letter the terms of which
prove their intimacy.

90 According to Georgios Cedrenos (flourished, eleventh /twelfth cen-
tury) , author of a world chronicle from the Creation to 1057, the oracle
of Apollon gav this answer:

"Tell the king, on earth has fallen the glorious dwelling,

"And the watersprings that spake are quenched and dead.

"Not a cell is left the God, no roof, no cover,

"In his hand the prophet laurel flowers no more."

(Swinburne's version in The Last Oracle). The sacred oracle foretold
the end of paganism!

If one wishes to understand how the Pythian prophetess functioned,
he should read Herbert William Parke, History of the Delphic Oracle
(Oxford, 1939; Isis 35, 250). A similar institution is still functioning today
in Tibet and was observed and described by Heinrich Harrer, Seven
Years in Tibet (pp. 180-82, London. 1953) .

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THE END OF GREEK SCIENCE AND CULTURE

confiscated Oribasios' estates and drove him into exile. Ori-
basios flourished for a time at the court of barbarian (Gothic?)
kings and distinguished himself so well that he was recalled to
Constantinople, c. 369. His goods were restituted to him and
he was permitted to continue his medical practice and writing.
He died c. 400.

He is a good example of the transition between paganism
and Christianity. It is possible that he had been brought up as
a Christian even as Julian was, but that under the latter's
ascendency his pagan feelings 21 were revived. According to
Eunapios (V-l) , he studied medicine under Zenon of Cypros, 22
and sat at the latter's feet at the Museum together with Magnos
of Antiocheia, the latrosophist. Both Zenon and Magnos were
pagans. Julian died too young (at thirty-two) to recant; Ori-
basios lived until- he was about seventy-five; we may safely as-
sume that he became a Christian again and died as such, for
paganism was no longer acceptable either in the empire or in
the barbarian kingdoms. His son Eustathios, to whom his
Synopsis is dedicated, was a Christian and a friend of St. Basil
(IV-2).

The purpose of Oribasios' Medical Collection is so well ex-

21

The word feelings is the correct one, for the main cause of attach-
ment to paganism was not rational but sentimental, the love of the
ancient cult and liturgy. The situation is similar to that of Catholics who
become Protestants, but in the course of time cannot bear any longer the
loss of sacramental aids and of the sacred liturgy and music, and return
to their original faith.

as Zenon was eventually driven out of the Museum by Georgios of
Cappadocia (Arian bishop of Alexandria, 356-61) but reinstated by
Julian. The founder of Stoicism, Zenon of Cition (IV-2 B.C.) is some-
times called Z6non of Cypros, but there can be no confusion between two
men separated by seven centuries.

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ANCIENT SCIENCE AND MODERN CIVILIZATION

plained at the beginning of it that it is best to quote his own
words:

Autocrator lulian, I have completed during our stay
in Western 23 Gaul the medical summary which your
Divinity had commanded me to prepare and which I have
drawn exclusively from the writings of Galen. After having
praised it, you commanded me to search for and put to-
gether all that is most important in the best medical books
and all that has contributed to attain the medical purpose.
I gladly undertook that work, being convinced that such a
collection would be very useful. ... As it would be super-
fluous arid even absurd to quote from the authors who have
written in the best manner and then again from those who
have not written as carefully, I shall take my materials ex-
clusively from the best authors, without omitting anything
which I first obtained from Galen, and I shall adapt my
own compilation to the fact of his superiority; Galen used
the best methods and the most exact definitions, because he
follows the Hippocratic principles and opinions. I shall
adopt the following order: hygiene and therapeutics, man's
nature and structure; conservation of health and its restora-
tion, diagnosis and prognosis; correction of diseases and
symptoms, etc.

My rough translation of the preface tells us the essential:
Julian was really Oribasios' patron and animator, and Galen
was the main source, to which every other source was sub-
ordinated. Galen's perfection was ascribed partly to the ex-
cellence of his own source, Hippocrates. Oribasios' references
to Galen are innumerable and his praise of him so frequent

13 Western Gaul as opposed to Eastern Gaul or Galatia in Anatolia,
with which Oribasios and Julian were more familiar. As Oribasios com-
pleted his summary in Gaul, we may assume that part of it at least was
written in Paris.

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THE END OF GREEK SCIENCE AND CULTURE

and emphatic that it established Galen's superiority as a kind
of medical dogma.

The books of the Synagogai which have come down to us
are Book I, 1-65, II, 1-27, Plant foods. II, 28-58, Animal
foods; 59-69, Milk, cheese, honey, horse flesh and flesh of
other solipeds, generalities. Ill, Various kinds of foods,
divided according to their physiological properties. IV,
Preparation of various kinds of food. V, Beverages. VI,
Physical exercises. VII, 1-22, Bloodletting. VII, 23-26, VIII,
Purgatives, diuretics, emetics, hemagogues. IX, 1-20, Air,
climates of various localities. IX, 21-55, External remedies,
such as fomentations, cataplasms, poultices, embrocations,
cupping. X, 1-9, Water, sand and air baths. X, 10-42, Ex-
ternal remedies. XI-XIII, Materia medica (copied verbatim
from Dioscorides but in alphabetical order). XIV-XV,
Simple drugs. XVI (only a short fragment), Composite
drugs. (XVI-XX lost.) XXI. Elements and temperaments.
XXII, Generation (XXIII lost.) XXIV, Internal organs,
from the brain to the sexual parts. XXV, Anatomical
nomenclature, Bones and muscles (57 chapters), Nerves
and vessels (4 chapters) .

XLIV, Inflammations, tumors, abscesses, fistulae, gang-
rene, erysipelas, herpes, boils. XLV, Tumors. XLVI, Frac-
tures. XLVII, Dislocations. XLVIII, Slings and bandages.
XLIX, Apparatus used to reduce luxations. L, Genito-
urinary troubles, Hernias. LI, Ulcers. (LII-LXX are lost.)

These books plus fragments from the lost ones were
edited in Greek and French by Ulco Cats Bussemaker and
Charles Victor Daremberg in four thick volumes (Paris,
1851-62). Two more volumes of the same magnificent edi-

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ANCIENT SCIENCE AND MODERN CIVILIZATION

tion were published posthumously by Auguste Molinier.
Vol. 5 (1873) contains Oribasios' Synopsis' 24 (medical sum-
mary) in nine books dedicated to his son Eustathios, and
his Euporisla (Remedia parabilia, home medicine) in four
books dedicated to Eunapios, plus ancient Latin versions
of the Synopsis and Latin additions to the Greek text. Vol.
6 (1876) contains more ancient Latin versions of the
Synopsis and Euporista and an elaborate index to the six
volumes.

It is well nigh impossible to assess the intrinisic merits of
such a bulky legacy as Oribasios' is. It gives us a clear idea of
the medical experience available in the second half of the
fourth century; that experience and knowledge were essentially
of pagan origin, and we may call Oribasios the last of the
pagan doctors as well as the first of the Byzantine age.

The Oribasios tradition was triple Latin, Greek and
Arabic. The Latin versions edited by Molinier (1873-76) go
back, some of them, to the sixth century; the earliest were
made in Ravenna during the Ostrogothic period (489-554) ;
others were made in the seventh and eighth centuries. These
Latin versions have transmitted to us parts of the text lost in
the original Greek. They were made when Oribasios was re-
latively modern and when relations between the Latin and
Greek worlds were still frequent.

The main tradition was Greek, however; the other By-
zantine physicians Aetios of Amida (VI-1), Alexandros of

24 Would this be a revised edition of the summary which Oribasios
completed for Julian in Gaul before the compilation of his Synagogai?
See Oribasios' preface quoted above.

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THE END OF GREEK SCIENCE AND CULTURE

Tralleis (Vl-2) , Paulos of Aigina (VI I- 1), etc., were to some
extent dependent upon it.

The Arabic tradition, instead of being anterior to the Latin
and the basis of it, was much posterior. The only Arabic
versions of Oribasios were made by 'Isa ibn Yahya (IX-2) and
perhaps by Stephanos, son of Basileios (IX-2). The Arabs paid
more attention to Aetios, Alexandros, and especially to Paulos
than to Oribasios, and even more to the latter's sources, Hip-
pocrates and Galen. Galen's extraordinary fame was built
up gradually by Oribasios, by the other Byzantine physicians,
by the Arabic ones and by Latin doctors of the thirteen century
and later; it reached its natural culmination during the
Renaissance.

There are no incunabula editions, but a number of Latin
editions appeared in the sixteenth century. Most of them were
restricted to a part of his writings but Giovanni Battista
Rasario attempted to publish the Opera omnia (Basel, Is-
ingrinius, 1557) ; reprinted in Paris, 1567. Greek editions were
fewer in number in the sixteenth century, partial and small.
The largest of the early Greek-Latin editions (Books I to XV
of the Collection) was prepared by Christian Friedrich de
Matthaei and published by the Imperial University of Moscow
(1808) . The first complete edition of the Greek text (as com-
plete as it could be) was the Greek-French edition of Busse-
maker, Darembergand Molinier (6 vols., Paris, 1851-76), which
has already been mentioned, because it is the most convenient.
A more critical edition of the Greek text is included in the
Corpus Medicorum Graecorum, Part VI, the Opera Omnia
edited by Joannes Raeder (1926-33). General indices are being
prepared by M. Haesler; in the meanwhile, the Greek-French
edition is indispensable.

95

ANCIENT SCIENCE AND MODERN CIVILIZATION

3. THE PHILOSOPHIC AND RELIGIOUS BACKGROUND

The reader may be astonished by the fact that most of the
men of science of whom I have spoken were pagans (or were
pagans most of the time) and exclaim, "How could that be
after more than three or four centuries of missionary efforts?"
The situation was extremely complex. 25 Philosophical teach-
ing continued; that teaching was essentially pagan, restricted
to Neoplatonism and mixed up with various forms of mystic-
ism. Stoicism was very strong but was also befouled with
Luperstitions.

The old mythology had become untenable, but the
mysteries, cults and liturgies were still popular among all
classes. As far as the educated and sophisticated people were
concerned, the myths were treasured only as a form of national
poetry but had been otherwise replaced by the astral religion,
which favored astrological delusions and was in turn fostered
by them. This was much too learned and too objective for the
common men and women who craved a living faith and a
religion which was personal, emotional, and colorful. Those
cravings were satisfied in varying degrees by a number of
oriental religions, 26 of which Christianity was for a long time
the least conspicuous. The development of Christianity, early
and late, is one of the mysteries of the world; it is the sacred
mystery in the highest sense. The events which guided the
Church and caused its final triumph in the face of innumerable
calamities are so incredible, or call them miraculous, that

25 The following discussion concerns only the Greek world, and this
means southeastern Europe and the Near East.

86 Masterly account of them by Franz Cumont, Les religions Orientates
dans le Paganisme Romain (4th ed., Paris, Geuthner, 1929; Isis 15, 271).

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THE END OF GREEK SCIENCE AND CULTURE

Christian apologists have used them as clinching proofs of the
truth and superiority of their faith.

One of the most astonishing factors is the pre-eminence in
the earliest times of the poorest people, those who were despis-
ed and downtrodden. The men who had the least amount of
social influence were the main agents of the revolution which
changed the whole world. It was only later arid very gradually
that men of substance joined the catechumens. That story is
so well known that I need not repeat it here. Let us make a
big jump to the time which we are now contemplating. It
was beautifully introduced by a woman of humble parentage,
the daughter, it is said, of an innkeeper, Helene, who became
the mistress of Constantios, a Roman officer. A child was
born to them at York, c. 274, named Constantine, and the
parents were then duly married, but when Constantios was
elevated to the Caesarship in 292, he was obliged to put her
aside in order to marry one who was more respectable. Con-
stantios Chloros was emperor from 305 to 306, his son Con-
stantine the Great, from 306 to 337.

Constantine was the first emperor to support Christianity.
In 313, he issued the Edict of Milan, securing toleration for
the Christians throughout the empire, and the official recog-
nition of Christendom occurred soon afterward. By 324,
Christian monograms became prominent on the coinage. Con-
stantine moved his capital away from Rome which was still
a stronghold of paganism and established it in 326 on the site
of Byzantion; the new city was called after himself, Con-
stantinople, inaugurated in 330 and dedicated to the Holy
Virgin. Constantine was called the Great; he was really a
little man, but he saw visions and took momentous decisions;
he caused the political success of Christianity and the relega-

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ANCIENT SCIENCE AND MODERN CIVILIZATION

tion of paganism, and he elaborated the comprehensive and
absolute authority of the Autocrator in church and state. His
many sins and crimes were washed away when he was bap-
tized by Eusebios of Caisareia (IV-1) not long before his death,
which occurred near Nicomedeia in 337; he was buried in his
own city, Constantinople.

It is possible that Constantine called his mother to the
imperial court in or after 306, and that after his own conver-
sion to Christianity in 312 he converted her (it is also said
that it was she who converted him) . Various crimes committed
by Constantine were probably the cause of her vow, when
already eighty years old, to make a pilgrimage to the Holy
Land. She accomplished the pilgrimage and discovered the
True Cross in Jerusalem, on the third of May, 326. 27 She died
not long afterwards, say in 327 or 328 (in Rome?); the places
of death and burial are not known. She never was an em-
press, even for a short time, but was eventually canonized
forever.

After Constantirie's death in 337, his three sons ordered the
murder of other members of the imperial family, but two of
his nephews, the brothers Gallos and Julian were spared. The
younger one, Julian, who interests us more deeply, vvas born
in Constantinople in 331. After his mother's untimely death,
he was put under the care of Eusebios, bishop of Nicomedeia, 28

"The feast of the Invention of the Cross (Inventio S. Cruets) is
celebrated on May 3. It is given far more importance by the Orthodox
churches than by the Catholic or Anglican.

28 Not to confuse Eusebios of Nicomedeia (d. 343) with Eusebios of
Caisareia (c. 265-340) , the historian, he who baptized Constantine the
Great in extremis. They were close contemporaries and both attended
the Council of Nicaia (325). Julian refers to the latter in his Letter to
the Galilaeans.

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THE END OF GREEK SCIENCE AND CULTURE

one of the most active defenders of Arianism. When Eusebios
died in 343, Julian was sent by the emperor to a castle in the
highlands of Cappadocia, where he remained six years in
solitary confinement. When his elder brother, Gallos, was
appointed Caesar in 35 1, 29 Julian was permitted to return to
Constantinople, where he continued his Hellenic and Chris-
tian studies. Soon afterwards, he was sent to Nicomedeia,
where he acted as lector (anagnostes) in the local churches,
yet was friendly with the sophist Libanios, whose lectures he
had been forbidden to attend. A little later, he went to
Pergamon, then to Ephesos to commune with Maximos, Neo-
platonic wonderworker and theurgist (Ihaiirnaturgos, thcurgos),
and it was probably in that sacred city that his apostasy was
completed. Julian was initiated to Mhhraism :m about the
year 352, for he. wrote in one of his letters that he had been a
Christian until his twentieth year; 31 his apostasy was kept
secret, however, tor ten years. The confusion of his mind is
shown by ihe fact that being in Athens in 355, he followed lec-
tures of the Christian teacher Prohairesios (St. Gregory Nazian-
zen and St. Basil being possibly among his classmates) and yet
was initiated to the Eleusinian mysteries. In the same year,
355, he was raised to the ranV of Caesar in Milano and then
ordered to Gaul to drive out the German invaders; in the

20 Gallos did not enjoy the Caesarship very long, for he was executed
by imperial order in 354.

30 The Persian god Mithras had been identified with Helios, Sol
invictus. Joseph Bidez has shown that Mithraist influences had been
operating in Julian's family, beginning with his grandfather, Constantios
Chloros. Therefore, Julian fancied that he was a descendant of Helios.
This helps to understand his apostasy. J. Bidez, "Julien 1'Apostat" (Revue
de ['instruction publique 57 [1914], 97-125, Bruxelles).

31 Letter 47 to the Alexandrians, 434 D (Loeb ed., 3, 149) .

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ANCIENT SCIENCE AND MODERN CIVILIZATION

course of that campaign he was able to redeem some 20,000
Gallic prisoners. Julian proved himself to be a good soldier,
a clever general and a capable administrator; he did so well
indeed that the emperor took umbrage at him and tried, in 360,
to withdraw part of his army, but the soldiers raised Julian
on their shields and nominated him their emperor. In January
361, he attended the feast of the Epiphany in Vienne (on the
Rhone) , then moved his army across Europe. During his
passage through Naisos 32 in the same year he addressed to the
Roman Senate and to the peoples of Sparta, Corinth and
Athens manifestoes proclaiming the revival of the Hellenic
religion. The rival emperor, Constantios, died and Julian
entered Constantinople as sole emperor at the very end of
the year. In the following year (362), he began his fateful
campaign against the Persians and was killed on the battle-
field, somewhere east of the Tigris, on 26 June 363, at the age
of thirty-two.

Julian had been all his life, with increasing fervor, an
enthusiastic lover of Hellenism; he was initiated into vari-
ous Greek and oriental mysteries, but as soon as he found
himself a soldier in the field he gave his full devotion to
Mithras, who was the favorite god of the Roman legions. On
4 February 362, he proclaimed religious freedom 83 and ordered
the restoration of the temples. He showed friendliness to the
Jews, restored Jerusalem to them and permitted them to re-
build the "Temple of the most high God"; the building had

88 Naisos or Nissa, Nish in eastern Yugoslavia, the very birthplace of
Constantine the Great in 306.

** Julian's edict of toleration of 362 was the counterpart of Constantine's
edict of half a century before (313) , but Constantine asked freedom of
religion for the Christians and Julian for the pagans. Constantine's edict
was slanted against the pagans, Julian's against the Christians.

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soon to be stopped, however, because of the earthquakes of
the winter 362-63 and of the Persian war. Julian tried to be,
if not impartial, at least tolerant, but as resistance to his
proselytism increased, he became impatient and more and
more intolerant. He gave special privileges to the pagans and
withdrew those which Christians had enjoyed. The main
troubles were caused by his efforts to suppress or restrict
Christian education. He would have liked to avoid violence,
but the old pagans who had never been Christians except in
name, if at all, as soon as they escaped Christian persecution,
naturally abused their new freedom and began their own
destruction of men and properties. One of their outstanding
victims was Georgios of Cappadocia, 34 the Arian bishop of
Alexandria, against whom great savings of hatred had ac-
cumulated because of his own persecutions. He ventured to
build a new church upon the ruins of a Mithraion and in-
furiated the populace; he was murdered and his body ignomin-
iously handled by the crazy mob. This happened on 24
December 361, that is, on the eve of the Mithriac feast, Natalis
invicti, now replaced by our Christmas.

34 In the Decline and Fall (chap. 23), Gibbon speaks very harshly of
him, concluding, "The odious stranger, disguising every circumstance of
time and place, assumed the mask of a martyr, a saint, and a Christian
hero, and the infamous George of Cappadocia has been transformed into
the renowned St. George of England, the patron of arms, of chivalry and
of the garter." Gibbon confused two different martyrs, Catholic and
Arian. St. George of England or George the Martyr, probably an officer
in Diocletian's army, was beheaded at Nicomedeia in 303, when Arian ism
did not yet exist (Areios began to teach his doctrine c. 318). George of
Cappadocia was an Arian; it is interesting to note that Julian seems to
have had more to do with Arians, as friends or adversaries, than with
Catholics.

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ANCIENT SCIENCE AND MODERN CIVILIZATION

As soon as Julian heard of this atrocious murder, he wrote
two letters (from Constantinople, January 362), one to the
Alexandrians to rebuke them mildly (he gave them "an advice
and arguments," paraincsin cai logus), the other to the Prefect
of Egypt, demanding Georgios' library, which he had had
occasion to use in his youth. This second letter does not con-
tain a word of regret or of blame for the murders. It is
disgraceful.

It is clear that in the end Julian's mind was distorted by
violent anti-Christian prejudices, yet he was, or had been, a
very intelligent man of superior morality. This is remarkable,
if one remembers the terrible vicissitudes of his life. 35

The last words ascribed to him, necicecas Galilaie (Thou
hast conquered, o Galileian), are legendary and paradoxical,
for he died at the head of an army which must have included
many Christian soldiers. The defeat of a Byzantine army by
Persian barbarians was a defeat for the empire which was still,
in spite of Julian's apostasy, a Christian empire.

Bibliography of Julian

Greek-Latin edition of Julian's works, Qiiae extant omnia
by Petrus Martinius and Carolus Cantoclarus, i.e., Pierre
Martini and Charles de Chanteclair (4 parts in 1 vol., Paris,
Duvallius, 1583).

The works of Julian were edited in Greek by Friedrich
Carl Hertlein (2 vols., Teubner, Leipzig, 1875-76), in Greek

35 The vicissitudes of Julian's life were so strange and momentous
that they soon became legendary. Richard Forster, "Kaiser Julian in der
Dichtung alter und neuer Zeit" (Studien zur vergleichenden Literaturge-
schichte 5, 1-120, Berlin, 1905). As to the modern literature inspired by
Julian's fate, it will suffice to recall the names of Voltaire, Alfred de Vigny,
Ibsen and Merezhkovski.

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THE END OF GREEK SCIENCE AND CULTURE

and English by Mrs. Wilmer Cave Wright 36 (Loeb Library,
3 vols., 1913-23); in Greek and French by Joseph Bidez (Assoc.
Guillaume Bude, Paris, 1924 if., Isis 7, 534) .

For the very interesting Syriac legend, see Georg Hoffmann,
Julianas der Abtriinnige, Syrische Erzdhlungen (Leiden, 1880).
Richard J. H. Gottheil: "A selection from the Syriac Julian
romance, with complete glossary in English and German"
(Semitic Study Series, no. 7, 112 pp., Leiden, 1906). Sir Her-
mann Gollancz, Julian the Apostate, now translated lor the
first time from the Syriac original (the only known manuscript
in the British Museum, edited by Hoffmann of Kiel) (264 pp.,
London, 1928).

It is impossible to know how much the Greek people were
influenced by Julian's apostasy. How many of them were un-
regenerated pagans, how many converted ones, how many born
Christians? How many temples had continued to function,
openly or secretly, before Julian's rule? How many churches
or monasteries were closed during it? The rule was too short
to do irreparable harm.

The period of Julian's life was one of great theological
activity because of the existence of various heresies. Not only
that, but one of the heresies, Arianism, was orthodoxy itself
during the greatest part of that time. It was condemned by
the Council of Nicaia, 87 325, then again by the Council of
Constantinople, 381; yet after the death of Constantine in 337,
it became the orthodox doctrine and remained so, roughly,
until 378. To be more precise, out of the fifty-six years

3e Professor in Bryn Mawr, died 1951 (Isis 43, 368).

87 Nicaia (= Nice, Isnik) was not far from Nicomedea, so often men-
tioned above. These were the two leading cities of Bithynia, disputing the
title of metropolis. Nicomedeia is at the east end of the Propontis (Sea of
Marmara), Nicaia at the east end of Lake Ascania, south of Nicomedeia.

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ANCIENT SCIENCE AND MODERN CIVILIZATION

separating the first two councils of the Church, forty were
years of Arian ascendency. Ulfilas, apostle of the Goths, was
consecrated bishop by Eusebios of Nicomedeia in 341, during
the Arian supremacy, and therefore the Gothic and other
Germanic tribes remained Arian for centuries.

Yet, the Catholic doctrine was very ably defended by the
Nicene and post-Nicene Fathers of the Church. Of the ten
generally mentioned, 38 no less than nine lived or began to live
during Julian's life. They are St. Athanasios of Alexandria
(d. 373), St. Basil of Cappadocia (d. 379), St. Gregory of
Nazianzos (d. 389), St. Gregory of Nyssa (d. 395) , St. Ambrose
of Treves (d. 397), St. Epiphanios of Palestine (d. 403), St.
John Chrysostom of Antioch (d. 407) , St. Jerome of Dalmatia
(d. 420), St. Augustine of Tagaste (d. 430). (The tenth one,
St. Cyril of Alexandria, was born only in 376, many years
after Julian's death; we shall come across him presently) . All
of these Fathers were Greek, except three of them, Ambrose,
Jerome and Augustine. Julian was well acquainted with at
least three of the Fathers, Athanasios, Basil and Gregory
Nazianzen. Athanasios was the main opponent of Arianism
from the beginning, and his life is the best symbol of the
ecclesiastical vicissitudes of that turbulent age. He was bishop
of Alexandria for forty-seven years, but spent about twenty
years away from his see, being exiled or driven into hiding
five times. We have recalled above that at the time of Julian's
accession, the very see of Alexandria was held by an Arian
bishop, Georgios of Cappadocia (bishop of Alexandria from
356 to 361) .

It is noteworthy that in spite of the fact that the Empire

38

E.g., in my Introduction (3, viii).
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THE END OF GREEK SCIENCE AND CULTURE

had become Christian soon after 313, the pagan schools con-
tinued to function, chiefly, the Academy of Athens and the
Museum of Alexandria. The Christians had their own schools,
but none had yet obtained a prestige comparable to that which
the pagan institutions enjoyed. In Alexandria, an ambitious
Christian school, the Didascaleion, had been made illustrious
by Clement of Alexandria (150-220) and Origen (IIM), but
it is doubtful whether it still flourished in the end of the fourth
century. The Museum, however, was thriving, and we have
already spoken of two illustrious teachers, Theon and his
daughter, Hypatia, the leading mathematicians of their time.
St. Cyril, who became bishop of Alexandria in 412, decided to
put an end to pagan and Jewish learning. He persecuted the
Jews and drove them out of the city. It was din ing his rule
that Hypatia was murdered by a Christian mob in 415. She
was dragged into a Christian church, entirely divested and her
body torn to pieces. Cyril died in 444, was canonized by Leo
XIII and proclaimed a Doctor of the Church. 39

Julian's apostasy and Hypatia's martyrdom are two drama-
tic events of very great significance, but we must be careful
not to misunderstand them as has been done repeatedly by
anti-clerical writers. Neither of them was a champion of free
thought. Julian was a Mithraist and a passionate defender of
Hellenism; his revival of paganism was a very queer one be-
cause it involved oriental religions of which the ancient Greeks
knew but little or nothing. He was a pagan mystic who ignored

80 St. Cyril of Alexandria (376-444) should not be confused with his
elder contemporary, St. Cyril of Jerusalem (c. 315-86) , who was Patriarch
of Jerusalem in 350, but was driven out by the Arians; he was permitted
to return to Jerusalem only in 379, and died there in 386. He took part
in the Council of Constantinople in 381.

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ANCIENT SCIENCE AND MODERN CIVILIZATION

the best part of rational Hellenism. It would not be fair to
reproach him for his neglect of Greek science, but even in the
field of morality, he was not well acquainted with the best
thought or did not understand it. He admired equally Alex-
ander the Great and Marcus Aurelius but was very remote
from both; his Persian campaign may have been inspired by
the first, but he never tried to continue Marcus' effort. He
liked virtue but lacked Marcus' passion for it, his deep kindness
and sanctity.

As to Hypatia, she was a Neoplatonist, not in any sense a
free thinker. She was very superior to Julian in that she
loved science more than myths; as a scientist, she was bound
to strive for objectivity and precision, while Julian was a man
of letters, a mystic and a mythomaniac. Socrates might be
called a martyr of freedom of thought; she was rather a martyr
of science, the first, or one of the first, known to us.

To understand fairly the attitude of both of them, one
must realize that in their time the defense of Hellenic tradi-
tions was the best rearguard action against Christian advance;
they were not so much anti-Christian as passionately Greek.

Jn this period of transition and spiritual travail, Hellen-
ism tried to take a religious form, and Christianity, a philoso-
phical one; Christianity was struggling hard to establish an
ecumenical orthodoxy against heretical distortions. They
could not meet, however, because it was impossible to accept
Christian doctrines without Christian faith, and the Greeks
were unwilling to abandon their mythological poetry, which
was the very core of Hellenism.

The educated pagans and the Christians were equally
capable of enthusiasm and ecstasy but their theological con-
ceptions were utterly incompatible.

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THE END OF G R E E K SCIENCE AND CULTURE

The general situation in the fourth and fifth centuries
was this. Whatever scientific work was done in the Greco-
Roman world was done chiefly, if not exclusively, by pagans.
In spite of Greek and oriental cults, the Church was gaining
ground steadily, but its unity was jeopardized by schisms.

The fundamental progress of the Church, without which
no later progress would have been possible, was due to the
generous faith of the humbler people. This is the best ex-
ample throughout the ages of the essential goodness of the
masses. By and by, men of substance joined the little men, and
finally the princes and rulers came in, but the Christian em-
perors were seldom good men; none was as good as Antoninus
Pius or Marcus Aurelius. In other words, even after Con-
stantine's recognition, the Church continued to be saved and
vindicated by saints and by men and women who were poor
and weak rather than rich and powerful.

As soon as Christianity was officially recognized in or soon
after 813, it was necessary to define the creed with greater
precision, and this was the source of endless difficulties. The
definition of each dogma was bound to instigate alternatives
in the minds of sophisticated theologians, quarrelsome and
vain, jealous of their spiritual authority. It was extremely
difficult, if not impossible, to reconcile on rational grounds
the notions of monotheism and Trinity; what were the rela-
tions of Jesus Christ to God and to man? Areios began to
preach c. 318 that God is absolutely unique and separate and
he denied the eternity and divinity of Christ. This heresy was
received so favorably by many clerks that Constantine was
compelled to summon the first Council at Nicaia in 325 in
order to discuss it and to push it out. The Nicene Creed re-
jected Arianism. In spite of that, Arianism enjoyed consider-

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ANCIENT SCIENCE AND MODERN CIVILIZATION

able popularity, was countenanced by emperors until 378, and
remained the orthodox doctrine of the Teutonic tribes for
centuries. It is very remarkable that that heresy, the first great
one, was so bold that the sixteenth century Socinianism and
later Unitarianism may be considered as stemming from it.

Arianism was condemned again by the second Council in
Constantinople in 381 and from that time on was driven out
of the Byzantine orthodoxy. New heresies diverged from the
accepted dogmas as to the nature of Christ in two opposite
directions. The orthodox view was, then and now, that there
are two natures in Christ (human and divine) but one person.
The followers of the Syrian priest, Nestorios (V-l) , claimed
that there are in Christ two natures and two persons. Eutyches,
archimandrite of a monastery near Constantinople, fought the
Nestorians so hard that he fell into the opposite error. He
created the heresy named after him Eutychianism and later
Monophysitism. Eutyches claimed that the divine and the
human are so blended in the person of Christ as to constitute
but one nature; Christ is of two natures but in one nature.
The Monophysites declared more bluntly that there is in
Christ but one nature and one person.

These Christological differences went very close to rending
apart the seamless coat of Christ. The various kinds of Chris-
tians hated one another more than they hated the infidels. The
Nestorian heresy was condemned by the third Council, in
Ephesos, 431; the fourth Council, in Chalcedon, 451, anathe-
matized the Eutychians as well as the Nestorians.

Condemnations and curses were rapidly enforced by eccles-
iastical and lay officials, and the final result was that many
good men were either killed or banished. We may assume that
men who prefer to abandon their homes and business and

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suffer all the rigors of poverty and exile rather than recant or
dissemble their religious thoughts that such men must be
exceptionally brave and good. The empire impoverished itself
to the profit of foreign countries. The Arians had been driven
westward; the Monophysites swarmed out into Syria and into
Egypt; the Nestorians emigrated eastward, and the school
of Edessa was their main center until it was closed by the em-
peror Zenon the Isaurian in 489. This caused a further dis-
persion of them; the Nestorian seat was in Seleuceia-Ctesiphon
in 498, in Baghdad in 762. They swarmed all over Asia as far
as the Pacific Ocean.

There was a medical school in Edessa, and the Nestorians
found themselves there in a scientific community. They trans-
lated many Greek books of philosophy and science into Syriac
and these Syrian books were later translated into Arabic. The
"scientific road" from Alexandria to Baghdad passed through
Edessa. 40 Thus would be completed in the fulness of time a
remarkable cycle. Greek science was born in Asia Minor, then
flourished in Greece proper, chiefly in Athens, then in Alex-
andria, and back to Asia, Pergamon, Constantinople, Edessa,
Baghdad.

The move from Athens to Alexandria was due to political
causes, that from Egypt and Greece to Asia very largely to re-
ligious ones. Every persecution is a centrifugal force. The
"good Christians" drove the Arians, Nestorians, Eutychians

40 It may be that when the school of Edessa (modern Urfa) was closed
in 489 some of the Nestorians took refuge at Jundlshapur in Khuzistan,
where a medical school was functioning; some of the pagans may have
resorted to the same place, which became a center of dispersion of
Greek culture in the Near East (Intro. 1, 435). JundishSpur is at a con-
siderable distance east of Baghdad, however.

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ANCIENT SCIENCE AND MODERN CIVILIZATION

further and further away and thus helped to diffuse Greek
science in the Asiatic world.

We have dealt so long with Christian sects that the reader
might forget the existence of pagans. There were still pagans,
especially among the least educated and the best educated
people. There were undoubtedly pagans (pagani, "rustics"
in the isolated places, and on the other hand, the "intellect-
uals," the outstanding philosophers, were reluctant to accept
Christianity and reject Hellenism. This was especially true
of those who were privileged to teach in the Academy of
Athens, which became, as it were, a center of resistance to the
new religion. Therefore, Justinian closed it in 529.

This is a fateful date, which I consider to be the best
symbol of the end of an age. The same year witnessed the
foundation of Monte Cassino by St. Benedict (Vl-1). Seven
teachers of the Academy escaped to the court of the king of
Persia, Chosroes, and remained there a few years until a treaty
of peace enabled them to return.

As to the empire itself, a part of its strength and of its vir-
tue was drained away by each persecution; some of the best
men were driven into exile some of the worst rose to the surface.

The final transition from paganism to Christianity was
difficult enough. It implied conflict of loyalties, the destruc-
tion of vested interests and the precarious establishment of
new ones. Moreover, the process was reversed during Julian's
reign. The situation was enormously aggravated, however,
by profound discords within the new Christian world. The
Arians went up and down, the Nestorians and the Mono-
physites were relentlessly persecuted. By the beginning of the
Sixth Century the Byzantine empire was weakened in many

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ways, chiefly because it had lost the good will of its own sub-
jects. The persecution of heterodoxies had been continued too
long, too many good people had been driven into sulkiness
and resentment or even into exile. Refugees carried Greek
science to the East and helped to prepare intellectual weapons
outside the Christian world, weapons which would soon be
used against it.

The Byzantine empire had finally become orthodox in
fact as well as in name, but it was totering; its material im-
proverishment was great, the spiritual one extreme. The time
would soon be ripe for Arabic conquests and no dike would
be strong enough to resist the Islamic flood.

Modern science is the continuation and fructification of
Greek science and would not exist without it. Our lectures
suggest another conclusion, however, which is more timely
today than it ever was.

Intolerance and persecution are self-defeating. The hunger
for knowledge and the search for truth can never be eradicated;
the best that persecution can do is to drive out non-conformists.
In the end this will be a loss not for humanity but for their
own country. The refugees carry wisdom and knowledge from
one place to another and mankind goes on.

Greek scholars were driven out of the Greek world and
helped to develop Arabic science. Later the Arabic writing
was translated into Latin, into Hebrew, and into our own
vernaculars. The treasure of Greek science, most of it at least,
came to us through that immense detour. We should be grate-
ful not only to the inventors, but also to all the men thanks
to those courage and obstinacy the ancient treasure finally
reached us and helped to make us what we are.

Ill

GEORGE SARTON

the History of Science at Harvard.

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